/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 x10 x2 x3 x4 x5 x6 x7 x8 x9)
(RULES
f(0,0,0,0,0,0,0,0,0,0) -> 0
f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,0,0,s(x10)) -> F(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,0,0,s(x10)) -> F(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,0,0,0,0,0,s(x10)) -> F(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,0,0,s(x10)) -> F(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 10

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,0,s(x9),x10) -> F(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 9

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,0,0,0,s(x8),x9,x10) -> F(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 8

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,0,0,s(x7),x8,x9,x10) -> F(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 7

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> F(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 6

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> F(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 5

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> F(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 4

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> F(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 3

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> F(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->->-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0,0,0,0,0,0,0,0,0,0) -> 0
 f(0,0,0,0,0,0,0,0,0,s(x10)) -> f(x10,x10,x10,x10,x10,x10,x10,x10,x10,x10)
 f(0,0,0,0,0,0,0,0,s(x9),x10) -> f(x9,x9,x9,x9,x9,x9,x9,x9,x9,x10)
 f(0,0,0,0,0,0,0,s(x8),x9,x10) -> f(x8,x8,x8,x8,x8,x8,x8,x8,x9,x10)
 f(0,0,0,0,0,0,s(x7),x8,x9,x10) -> f(x7,x7,x7,x7,x7,x7,x7,x8,x9,x10)
 f(0,0,0,0,0,s(x6),x7,x8,x9,x10) -> f(x6,x6,x6,x6,x6,x6,x7,x8,x9,x10)
 f(0,0,0,0,s(x5),x6,x7,x8,x9,x10) -> f(x5,x5,x5,x5,x5,x6,x7,x8,x9,x10)
 f(0,0,0,s(x4),x5,x6,x7,x8,x9,x10) -> f(x4,x4,x4,x4,x5,x6,x7,x8,x9,x10)
 f(0,0,s(x3),x4,x5,x6,x7,x8,x9,x10) -> f(x3,x3,x3,x4,x5,x6,x7,x8,x9,x10)
 f(0,s(x2),x3,x4,x5,x6,x7,x8,x9,x10) -> f(x2,x2,x3,x4,x5,x6,x7,x8,x9,x10)
 f(s(x1),x2,x3,x4,x5,x6,x7,x8,x9,x10) -> f(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.