YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(0(x1:S)))
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(5(1(x1:S))))) -> 5#(1(0(0(0(x1:S)))))
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(2(0(x1:S)))
 0#(0(0(1(x1:S)))) -> 0#(2(1(0(0(x1:S)))))
 0#(0(0(1(x1:S)))) -> 0#(2(1(0(2(0(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(2(5(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(2(5(2(0(x1:S))))))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(2(5(1(0(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(2(5(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(2(1(0(5(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(2(1(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(2(1(2(5(0(x1:S))))))
 0#(0(5(1(x1:S)))) -> 0#(2(1(4(5(0(x1:S))))))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(2(1(0(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(1(0(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(1(0(x1:S)))
 0#(0(5(1(x1:S)))) -> 5#(2(0(x1:S)))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 5#(1(0(0(x1:S))))
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(5(0(x1:S))))) -> 0#(5(0(2(1(0(x1:S))))))
 0#(0(1(5(0(x1:S))))) -> 0#(2(5(1(0(0(x1:S))))))
 0#(0(1(5(0(x1:S))))) -> 0#(2(1(0(x1:S))))
 0#(0(1(5(0(x1:S))))) -> 5#(0(2(1(0(x1:S)))))
 0#(0(1(5(0(x1:S))))) -> 5#(1(0(0(x1:S))))
 0#(0(1(1(x1:S)))) -> 0#(1(2(1(0(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(2(0(1(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(2(0(1(x1:S))))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(2(1(0(4(0(x1:S))))))
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(1(2(2(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(0(3(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(0(4(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(2(5(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(5(1(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(1(0(4(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(1(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(1(2(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(2(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(3(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(3(1(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(2(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(1(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(2(0(x1:S))))
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(1(x1:S))) -> 5#(1(0(x1:S)))
 0#(0(3(1(x1:S)))) -> 0#(1(3(0(x1:S))))
 0#(0(3(1(x1:S)))) -> 0#(2(0(3(x1:S))))
 0#(0(3(1(x1:S)))) -> 0#(2(1(0(x1:S))))
 0#(0(3(1(x1:S)))) -> 0#(2(3(1(0(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(0(4(1(0(5(x1:S))))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 0#(4(1(0(5(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(0(2(1(2(5(x1:S))))))
 0#(5(0(1(x1:S)))) -> 0#(1(5(2(0(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(1(2(0(2(5(x1:S))))))
 0#(5(0(1(x1:S)))) -> 0#(1(2(5(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(2(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(2(5(0(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(2(5(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(2(1(5(0(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(2(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(2(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(2(0(x1:S)))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(2(5(2(5(x1:S))))))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(2(5(5(x1:S))))
 0#(5(5(1(x1:S)))) -> 0#(2(5(1(5(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(1(0(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(1(0(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(1(5(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(2(5(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(2(5(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(1(0(x1:S)))
 0#(5(1(1(x1:S)))) -> 5#(1(2(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(1(2(1(0(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(2(1(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(2(5(x1:S)))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(1(3(0(x1:S))))
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(1(1(3(2(0(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(2(0(1(x1:S))))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(1(x1:S)))) -> 5#(1(0(0(x1:S))))
 0#(1(0(3(1(x1:S))))) -> 0#(1(3(1(0(x1:S)))))
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 5#(1(0(0(x1:S))))
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(2(0(x1:S)))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(5(1(1(x1:S))))) -> 5#(1(0(3(x1:S))))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 0#(2(1(4(5(x1:S)))))
 0#(4(5(5(1(x1:S))))) -> 5#(0(2(1(4(5(x1:S))))))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(2(0(x1:S)))
 5#(0(0(1(x1:S)))) -> 0#(2(5(1(0(x1:S)))))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(0(1(x1:S)))) -> 5#(0(2(0(x1:S))))
 5#(0(0(1(x1:S)))) -> 5#(1(0(2(0(x1:S)))))
 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S)))
 5#(0(0(1(x1:S)))) -> 5#(2(0(0(x1:S))))
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 5#(1(2(1(0(0(x1:S))))))
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(0(x1:S)))
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(5(1(x1:S))))) -> 5#(1(0(0(0(x1:S)))))
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(2(0(x1:S)))
 0#(0(0(1(x1:S)))) -> 0#(2(1(0(0(x1:S)))))
 0#(0(0(1(x1:S)))) -> 0#(2(1(0(2(0(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(2(5(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(2(5(2(0(x1:S))))))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(2(5(1(0(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(2(5(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(2(1(0(5(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(2(1(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(2(1(2(5(0(x1:S))))))
 0#(0(5(1(x1:S)))) -> 0#(2(1(4(5(0(x1:S))))))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(2(1(0(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(1(0(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(1(0(x1:S)))
 0#(0(5(1(x1:S)))) -> 5#(2(0(x1:S)))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 5#(1(0(0(x1:S))))
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(5(0(x1:S))))) -> 0#(5(0(2(1(0(x1:S))))))
 0#(0(1(5(0(x1:S))))) -> 0#(2(5(1(0(0(x1:S))))))
 0#(0(1(5(0(x1:S))))) -> 0#(2(1(0(x1:S))))
 0#(0(1(5(0(x1:S))))) -> 5#(0(2(1(0(x1:S)))))
 0#(0(1(5(0(x1:S))))) -> 5#(1(0(0(x1:S))))
 0#(0(1(1(x1:S)))) -> 0#(1(2(1(0(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(2(0(1(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(2(0(1(x1:S))))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(2(1(0(4(0(x1:S))))))
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(1(2(2(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(0(3(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(0(4(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(2(5(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(5(1(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(1(0(4(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(1(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(1(2(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(2(2(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(3(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(2(3(1(0(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(2(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(1(0(x1:S))))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(2(0(x1:S))))
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(1(x1:S))) -> 5#(1(0(x1:S)))
 0#(0(3(1(x1:S)))) -> 0#(1(3(0(x1:S))))
 0#(0(3(1(x1:S)))) -> 0#(2(0(3(x1:S))))
 0#(0(3(1(x1:S)))) -> 0#(2(1(0(x1:S))))
 0#(0(3(1(x1:S)))) -> 0#(2(3(1(0(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(0(4(1(0(5(x1:S))))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 0#(4(1(0(5(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(0(2(1(2(5(x1:S))))))
 0#(5(0(1(x1:S)))) -> 0#(1(5(2(0(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(1(2(0(2(5(x1:S))))))
 0#(5(0(1(x1:S)))) -> 0#(1(2(5(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(2(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(2(5(0(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(2(5(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(2(1(5(0(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(2(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(2(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(2(0(x1:S)))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(2(5(2(5(x1:S))))))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(2(5(5(x1:S))))
 0#(5(5(1(x1:S)))) -> 0#(2(5(1(5(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(1(0(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(1(0(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(1(5(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(2(5(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(2(5(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(1(0(x1:S)))
 0#(5(1(1(x1:S)))) -> 5#(1(2(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(1(2(1(0(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(2(1(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(2(5(x1:S)))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(1(3(0(x1:S))))
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(1(1(3(2(0(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(2(0(1(x1:S))))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(1(x1:S)))) -> 5#(1(0(0(x1:S))))
 0#(1(0(3(1(x1:S))))) -> 0#(1(3(1(0(x1:S)))))
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 5#(1(0(0(x1:S))))
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(2(0(x1:S)))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(5(1(1(x1:S))))) -> 5#(1(0(3(x1:S))))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 0#(2(1(4(5(x1:S)))))
 0#(4(5(5(1(x1:S))))) -> 5#(0(2(1(4(5(x1:S))))))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(2(0(x1:S)))
 5#(0(0(1(x1:S)))) -> 0#(2(5(1(0(x1:S)))))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(0(1(x1:S)))) -> 5#(0(2(0(x1:S))))
 5#(0(0(1(x1:S)))) -> 5#(1(0(2(0(x1:S)))))
 5#(0(0(1(x1:S)))) -> 5#(1(0(x1:S)))
 5#(0(0(1(x1:S)))) -> 5#(2(0(0(x1:S))))
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 5#(1(2(1(0(0(x1:S))))))
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(0(x1:S)))
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(0(x1:S)))
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 2
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(5(1(x1:S))))) -> 0#(x1:S)
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(0(1(2(0(2(x1:S))))))
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(1(x1:S)))) -> 0#(x1:S)
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 1
[5](X) = 2.X + 1
[1](X) = 2.X + 1
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = X + 1
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(5(0(1(x1:S))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(1(x1:S))))) -> 5#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 2
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(5(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(4(5(0(x1:S))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 0#(x1:S)
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = X + 2
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X
[5](X) = 2.X + 2
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(0(x1:S))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(1(x1:S)))) -> 5#(x1:S)
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(3(1(x1:S))))) -> 0#(0(x1:S))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X
[5](X) = 2.X + 2
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(5(3(1(x1:S))))) -> 0#(x1:S)
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 2
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(5(0(x1:S))))) -> 0#(0(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X
[5](X) = 2.X + 1
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(1(x1:S)))) -> 0#(x1:S)
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(4(0(x1:S))))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(3(x1:S))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(4(0(x1:S)))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(4(x1:S))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 0#(x1:S)
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(1(x1:S))) -> 5#(0(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(5(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(2(x1:S))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(1(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(1(2(2(x1:S))))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(2(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(1(0(1(x1:S))))) -> 0#(0(1(1(1(3(x1:S))))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(3(x1:S))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 1
[5](X) = 2.X + 1
[1](X) = 2.X + 1
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(0(3(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(0(1(x1:S))))) -> 0#(0(0(1(x1:S))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(0(1(x1:S))))) -> 5#(0(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 1
[5](X) = 2.X
[1](X) = 2.X + 1
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 0#(5(x1:S))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 1
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(0(x1:S))))) -> 5#(x1:S)
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 1
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = X + 2
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 0#(x1:S)
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = X + 2
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(2(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 1
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(0(1(x1:S))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(0(1(x1:S)))) -> 5#(x1:S)
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(5(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X
[5](X) = 2.X + 1
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 0#(x1:S)
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(0(5(1(x1:S))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(0(1(x1:S)))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(5(x1:S))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(5(1(x1:S)))) -> 5#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 0#(1(5(0(x1:S))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 0#(x1:S)
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 1
[1](X) = 2.X + 1
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(0(1(x1:S))))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(1(x1:S))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(4(5(x1:S)))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 0#(x1:S)
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 1
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 1
[0#](X) = 2.X + 1
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(0(1(1(x1:S))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 1
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(0(x1:S))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 1
[5#](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(1(1(x1:S)))) -> 5#(x1:S)
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(0(1(x1:S))))) -> 0#(5(1(x1:S)))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(0(1(x1:S))))) -> 0#(3(0(5(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 1
[0#](X) = 2.X + 1
[5#](X) = X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 0#(x1:S)
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(5(3(1(1(x1:S))))) -> 5#(x1:S)
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = X + 2
[5#](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(1(x1:S)))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(0(x1:S))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(1(x1:S)))) -> 0#(x1:S)
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(0(3(1(x1:S))))) -> 0#(x1:S)
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(5(0(1(x1:S))))) -> 0#(0(x1:S))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(5(0(1(x1:S))))) -> 0#(x1:S)
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 0#(1(4(1(1(x1:S))))) -> 0#(1(x1:S))
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Projection:
 pi(0#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 0#(0(3(1(x1:S))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 0#(3(1(x1:S)))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X + 2
[0#](X) = 2.X + 1
[5#](X) = X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(5(1(x1:S))))) -> 5#(0(0(3(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(0(1(x1:S)))) -> 0#(x1:S)
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(5(1(1(x1:S))))) -> 0#(3(x1:S))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = X
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(3(1(0(1(x1:S))))) -> 0#(0(1(x1:S)))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X
[1](X) = 2.X + 1
[2](X) = 0
[3](X) = X
[4](X) = X + 1
[0#](X) = X + 1
[5#](X) = 2.X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(0(0(3(1(x1:S))))) -> 0#(3(0(0(1(x1:S)))))
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(4(5(5(1(x1:S))))) -> 5#(x1:S)
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[5](X) = 2.X + 2
[1](X) = 2.X + 2
[2](X) = 0
[3](X) = X
[4](X) = X
[0#](X) = 2.X + 2
[5#](X) = 2.X + 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(0(x1:S))
 5#(0(0(1(x1:S)))) -> 0#(x1:S)
 5#(0(1(0(1(x1:S))))) -> 0#(0(x1:S))
 5#(0(1(0(1(x1:S))))) -> 0#(x1:S)
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
->->-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 0#(4(4(1(1(x1:S))))) -> 0#(4(x1:S))
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[1](X) = 2.X
[4](X) = 2.X + 2
[0#](X) = 2.X

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(0(0(5(1(x1:S))))) -> 2(5(1(0(0(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(0(1(2(0(2(x1:S))))))
 0(0(0(1(x1:S)))) -> 0(2(1(0(2(0(x1:S))))))
 0(0(0(1(x1:S)))) -> 2(0(2(1(0(0(x1:S))))))
 0(0(0(3(1(x1:S))))) -> 2(0(3(0(0(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 0(0(2(5(1(1(x1:S))))))
 0(0(5(1(1(x1:S))))) -> 2(1(0(5(0(1(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(5(0(2(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(1(2(5(2(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(5(1(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 0(2(1(2(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 0(2(1(4(5(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 1(2(0(0(2(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(0(2(1(0(5(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(5(0(2(1(0(x1:S))))))
 0(0(5(1(x1:S)))) -> 2(5(1(0(0(x1:S)))))
 0(0(5(1(x1:S)))) -> 2(1(0(4(5(0(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(0(0(2(5(1(x1:S))))))
 0(0(5(3(1(x1:S))))) -> 3(2(5(1(0(0(x1:S))))))
 0(0(1(0(x1:S)))) -> 0(0(2(0(2(1(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(5(0(2(1(0(x1:S))))))
 0(0(1(5(0(x1:S))))) -> 0(2(5(1(0(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(1(2(1(0(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(0(2(0(1(1(x1:S))))))
 0(0(1(1(x1:S)))) -> 2(1(0(2(0(1(x1:S))))))
 0(0(1(4(0(x1:S))))) -> 0(2(1(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(3(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(4(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 1(2(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(2(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(0(3(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(5(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(3(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 1(2(3(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 1(3(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(0(2(1(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(5(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(4(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(1(0(x1:S)))))
 0(0(1(x1:S))) -> 2(0(2(1(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(2(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(0(x1:S)))))
 0(0(1(x1:S))) -> 2(1(0(2(5(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(0(2(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(2(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 2(1(4(0(4(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(2(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(0(4(1(0(x1:S))))))
 0(0(1(x1:S))) -> 2(2(1(0(2(0(x1:S))))))
 0(0(1(x1:S))) -> 3(1(2(0(2(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(2(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(0(1(3(0(x1:S)))))
 0(0(3(1(x1:S)))) -> 2(0(2(3(1(0(x1:S))))))
 0(0(3(1(x1:S)))) -> 2(1(0(2(0(3(x1:S))))))
 0(0(3(1(x1:S)))) -> 3(2(0(2(1(0(x1:S))))))
 0(5(0(0(1(x1:S))))) -> 2(5(0(0(0(1(x1:S))))))
 0(5(0(1(0(x1:S))))) -> 0(0(4(1(0(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(5(2(1(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(0(2(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 0(1(2(0(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 1(2(0(2(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(0(1(2(5(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(1(5(2(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(0(2(1(5(0(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(2(x1:S))))))
 0(5(0(1(x1:S)))) -> 2(5(0(0(1(x1:S)))))
 0(5(0(1(x1:S)))) -> 2(5(0(2(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 0(1(2(5(2(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 1(2(0(2(5(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(0(2(5(1(5(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(0(2(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(5(5(1(0(x1:S)))))
 0(5(5(1(x1:S)))) -> 2(5(2(5(0(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(0(5(1(x1:S))))))
 0(5(5(1(x1:S)))) -> 2(2(5(5(1(0(x1:S))))))
 0(5(1(0(1(x1:S))))) -> 2(1(0(1(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(5(1(0(x1:S)))))
 0(5(1(1(x1:S)))) -> 1(2(1(0(4(5(x1:S))))))
 0(5(1(1(x1:S)))) -> 1(2(1(4(5(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(0(1(2(5(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(0(1(1(x1:S)))))
 0(5(1(1(x1:S)))) -> 2(5(0(2(1(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(0(1(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(1(2(1(0(x1:S))))))
 0(5(1(1(x1:S)))) -> 2(5(2(1(0(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(0(1(3(1(x1:S))))))
 0(5(1(3(1(x1:S))))) -> 2(5(1(0(1(3(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(0(2(5(5(1(x1:S))))))
 0(5(2(5(1(x1:S))))) -> 2(5(5(0(2(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(5(3(0(1(x1:S))))) -> 2(0(3(0(5(1(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(1(3(0(2(5(x1:S))))))
 0(5(3(1(1(x1:S))))) -> 1(2(5(1(3(0(x1:S))))))
 0(5(4(1(1(x1:S))))) -> 2(5(0(4(1(1(x1:S))))))
 0(1(0(1(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(1(2(2(x1:S))))))
 0(1(0(1(x1:S)))) -> 0(0(1(2(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 0(1(1(3(2(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(1(3(2(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(0(2(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 1(2(1(0(0(x1:S)))))
 0(1(0(1(x1:S)))) -> 1(2(2(0(0(1(x1:S))))))
 0(1(0(1(x1:S)))) -> 2(1(0(0(1(x1:S)))))
 0(1(0(1(x1:S)))) -> 2(1(2(1(0(0(x1:S))))))
 0(1(0(1(x1:S)))) -> 3(1(2(1(0(0(x1:S))))))
 0(1(0(3(1(x1:S))))) -> 2(0(1(3(1(0(x1:S))))))
 0(1(5(0(1(x1:S))))) -> 1(2(5(1(0(0(x1:S))))))
 0(1(1(0(1(x1:S))))) -> 0(0(1(1(1(3(x1:S))))))
 0(1(4(1(1(x1:S))))) -> 1(2(1(4(0(1(x1:S))))))
 0(3(0(5(1(x1:S))))) -> 2(5(0(0(3(1(x1:S))))))
 0(3(0(1(x1:S)))) -> 1(2(3(0(2(0(x1:S))))))
 0(3(0(1(x1:S)))) -> 3(1(2(0(2(0(x1:S))))))
 0(3(5(0(1(x1:S))))) -> 0(0(3(2(5(1(x1:S))))))
 0(3(5(1(1(x1:S))))) -> 1(2(5(1(0(3(x1:S))))))
 0(3(1(0(1(x1:S))))) -> 2(3(1(0(0(1(x1:S))))))
 0(4(5(5(1(x1:S))))) -> 5(0(2(1(4(5(x1:S))))))
 0(4(4(1(1(x1:S))))) -> 1(2(1(4(0(4(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(2(5(2(0(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 1(4(5(0(2(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(0(2(5(1(0(x1:S))))))
 5(0(0(1(x1:S)))) -> 2(5(1(0(2(0(x1:S))))))
 5(0(1(0(1(x1:S))))) -> 5(1(2(1(0(0(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 1(4(5(2(5(1(x1:S))))))
 5(5(4(1(1(x1:S))))) -> 2(5(1(4(5(1(x1:S))))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.