/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x1)
(RULES
0(q1(1(x1))) -> q2(0(1'(x1)))
0(q2(0(x1))) -> q2(0(0(x1)))
0(q2(1'(x1))) -> q2(0(1'(x1)))
0'(q1(1(x1))) -> q2(0'(1'(x1)))
0'(q2(0(x1))) -> q2(0'(0(x1)))
0'(q2(1'(x1))) -> q2(0'(1'(x1)))
1'(q1(1(x1))) -> q2(1'(1'(x1)))
1'(q2(0(x1))) -> q2(1'(0(x1)))
1'(q2(1'(x1))) -> q2(1'(1'(x1)))
q0(0(x1)) -> 0'(q1(x1))
q0(1'(x1)) -> 1'(q3(x1))
q1(0(x1)) -> 0(q1(x1))
q1(1'(x1)) -> 1'(q1(x1))
q2(0'(x1)) -> 0'(q0(x1))
q3(1'(x1)) -> 1'(q3(x1))
q3(b(x1)) -> b(q4(x1))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 0#(q1(1(x1))) -> 0#(1'(x1))
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q1(1(x1))) -> 0#(1'(x1))
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q1(1(x1))) -> 0#(1'(x1))
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q1(1(x1))) -> 0#(1'(x1))
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 2
[1](X) = 2.X + 2
[b](X) = X + 2
[q4](X) = 2.X + 2
[0#](X) = 2.X
[0'#](X) = 2.X
[1'#](X) = 2.X
[Q0](X) = 2.X + 2
[Q1](X) = 2.X
[Q2](X) = 2.X
[Q3](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q1(1(x1))) -> 1'#(x1)
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = X
[1'](X) = 2.X + 2
[q0](X) = 2.X + 1
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = 0
[q4](X) = 2
[0#](X) = 2.X + 2
[0'#](X) = X + 1
[1'#](X) = 2.X + 2
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q1(1(x1))) -> Q2(0(1'(x1)))
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 2
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = 1
[0#](X) = 2.X + 2
[0'#](X) = 2.X + 1
[1'#](X) = 2.X + 1
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 1
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q2(0(x1))) -> 0#(0(x1))
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X
[1'](X) = X
[q0](X) = 2.X
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X
[1](X) = 2.X + 2
[b](X) = X + 2
[q4](X) = X + 2
[0#](X) = 2.X + 2
[0'#](X) = 2.X + 1
[1'#](X) = X
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q2(0(x1))) -> Q2(0(0(x1)))
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = 2.X
[q4](X) = 2.X
[0#](X) = 2.X + 2
[0'#](X) = X + 2
[1'#](X) = X + 2
[Q0](X) = X + 2
[Q1](X) = 2.X + 2
[Q2](X) = X + 2
[Q3](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q2(1'(x1))) -> 0#(1'(x1))
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = X
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 2
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = 2.X + 2
[0#](X) = 2.X + 2
[0'#](X) = 2.X + 2
[1'#](X) = X
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0#(q2(1'(x1))) -> Q2(0(1'(x1)))
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 1
[0'](X) = 2
[1'](X) = 1
[q0](X) = 2
[q1](X) = 1
[q2](X) = X
[q3](X) = X
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = X
[0#](X) = 2.X
[0'#](X) = 2
[1'#](X) = 2
[Q0](X) = 2
[Q1](X) = 2
[Q2](X) = X
[Q3](X) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> 0#(q1(x1))
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q1(1(x1))) -> 0'#(1'(x1))
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 2
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = 2.X + 2
[0'#](X) = X + 2
[1'#](X) = X + 2
[Q0](X) = 2.X + 1
[Q1](X) = 2.X + 1
[Q2](X) = X + 2
[Q3](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q1(1(x1))) -> 1'#(x1)
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 2
[1](X) = 2.X + 2
[b](X) = X + 2
[q4](X) = 2.X + 2
[0'#](X) = X + 2
[1'#](X) = X + 2
[Q0](X) = 2.X + 2
[Q1](X) = X + 2
[Q2](X) = X + 2
[Q3](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q1(1(x1))) -> Q2(0'(1'(x1)))
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 1
[0'](X) = 2.X + 1
[1'](X) = X + 1
[q0](X) = X
[q1](X) = X
[q2](X) = X
[q3](X) = X
[1](X) = 2.X + 2
[b](X) = 2.X + 1
[q4](X) = X
[0'#](X) = 2.X + 1
[1'#](X) = 2.X + 2
[Q0](X) = 2.X + 1
[Q1](X) = 2.X + 2
[Q2](X) = X
[Q3](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q2(0(x1))) -> 0'#(0(x1))
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X
[1'](X) = 2.X + 2
[q0](X) = 2.X
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = 2
[q4](X) = 0
[0'#](X) = 2.X
[1'#](X) = 2.X + 1
[Q0](X) = 2.X + 1
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 1
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q2(0(x1))) -> Q2(0'(0(x1)))
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 1
[0'](X) = 2.X
[1'](X) = 2.X + 1
[q0](X) = 2.X + 1
[q1](X) = 2.X + 1
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = X + 2
[q4](X) = 2.X + 2
[0'#](X) = 2.X
[1'#](X) = 2.X + 2
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q2(1'(x1))) -> 0'#(1'(x1))
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 2.X + 1
[q0](X) = 2.X + 2
[q1](X) = 2.X + 1
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = 2.X + 1
[0'#](X) = 2.X + 2
[1'#](X) = 2.X
[Q0](X) = 2.X + 1
[Q1](X) = 2.X
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 0'#(q2(1'(x1))) -> Q2(0'(1'(x1)))
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X
[1'](X) = 2.X + 2
[q0](X) = 2.X + 1
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = 2.X + 1
[0'#](X) = 2.X
[1'#](X) = 2.X + 2
[Q0](X) = 2.X + 1
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> 0'#(q1(x1))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> 0'#(q0(x1))
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q1(1(x1))) -> 1'#(1'(x1))
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = X
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 2
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = X + 2
[1'#](X) = X
[Q0](X) = X
[Q1](X) = X + 1
[Q2](X) = X
[Q3](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q1(1(x1))) -> 1'#(x1)
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = X
[1'](X) = 2.X + 2
[q0](X) = X
[q1](X) = 2.X + 2
[q2](X) = X
[q3](X) = X
[1](X) = 2.X
[b](X) = 2.X + 1
[q4](X) = X
[1'#](X) = 2.X + 2
[Q0](X) = X
[Q1](X) = 2.X + 2
[Q2](X) = X
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q1(1(x1))) -> Q2(1'(1'(x1)))
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X + 2
[1'](X) = 0
[q0](X) = X
[q1](X) = X
[q2](X) = X
[q3](X) = 2.X
[1](X) = X + 2
[b](X) = X + 2
[q4](X) = 2.X + 2
[1'#](X) = 2
[Q0](X) = 2
[Q1](X) = 2
[Q2](X) = 2.X + 1
[Q3](X) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q2(0(x1))) -> 1'#(0(x1))
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = 2.X
[1'](X) = 2.X + 2
[q0](X) = 2.X
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = 2.X + 1
[1](X) = 2.X + 2
[b](X) = 2.X + 2
[q4](X) = 2.X + 1
[1'#](X) = 2.X + 1
[Q0](X) = 2.X
[Q1](X) = 2.X + 2
[Q2](X) = X + 2
[Q3](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q2(0(x1))) -> Q2(1'(0(x1)))
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X
[0'](X) = X
[1'](X) = 2.X
[q0](X) = X + 1
[q1](X) = 2.X
[q2](X) = 2.X + 2
[q3](X) = 0
[1](X) = 2.X + 2
[b](X) = 2.X
[q4](X) = 0
[1'#](X) = 2.X
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 2
[Q3](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q2(1'(x1))) -> 1'#(1'(x1))
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 1
[0'](X) = 2.X + 2
[1'](X) = X
[q0](X) = 2.X + 1
[q1](X) = X
[q2](X) = 2.X + 2
[q3](X) = X
[1](X) = 2.X + 2
[b](X) = 2.X + 1
[q4](X) = X
[1'#](X) = 2.X + 1
[Q0](X) = 2.X + 2
[Q1](X) = 2.X + 1
[Q2](X) = 2.X + 2
[Q3](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 1'#(q2(1'(x1))) -> Q2(1'(1'(x1)))
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
-> Usable rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0](X) = 2.X + 2
[0'](X) = X
[1'](X) = 2.X + 2
[q0](X) = 2.X + 2
[q1](X) = 2.X + 2
[q2](X) = 2.X + 2
[q3](X) = X
[1](X) = 2.X + 2
[b](X) = 0
[q4](X) = 2.X + 2
[1'#](X) = 2.X + 2
[Q0](X) = 2.X + 1
[Q1](X) = 2.X + 2
[Q2](X) = 2.X + 1
[Q3](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 Q0(0(x1)) -> Q1(x1)
 Q0(1'(x1)) -> 1'#(q3(x1))
 Q0(1'(x1)) -> Q3(x1)
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> 1'#(q1(x1))
 Q1(1'(x1)) -> Q1(x1)
 Q2(0'(x1)) -> Q0(x1)
 Q3(1'(x1)) -> 1'#(q3(x1))
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 Q3(1'(x1)) -> Q3(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->->Cycle:
->->-> Pairs:
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> Q1(x1)
->->-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 Q3(1'(x1)) -> Q3(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Projection:
 pi(Q3) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 Q1(0(x1)) -> Q1(x1)
 Q1(1'(x1)) -> Q1(x1)
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Projection:
 pi(Q1) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q0(0(x1)) -> 0'(q1(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 q2(0'(x1)) -> 0'(q0(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.