/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.