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


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YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
max(L(x:S)) -> x:S
max(N(L(0),L(y:S))) -> y:S
max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 MAX(N(L(s(x:S)),L(s(y:S)))) -> MAX(N(L(x:S),L(y:S)))
 MAX(N(L(x:S),N(y:S,z:S))) -> MAX(N(L(x:S),L(max(N(y:S,z:S)))))
 MAX(N(L(x:S),N(y:S,z:S))) -> MAX(N(y:S,z:S))
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))

Problem 1: 

SCC Processor:
-> Pairs:
 MAX(N(L(s(x:S)),L(s(y:S)))) -> MAX(N(L(x:S),L(y:S)))
 MAX(N(L(x:S),N(y:S,z:S))) -> MAX(N(L(x:S),L(max(N(y:S,z:S)))))
 MAX(N(L(x:S),N(y:S,z:S))) -> MAX(N(y:S,z:S))
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MAX(N(L(s(x:S)),L(s(y:S)))) -> MAX(N(L(x:S),L(y:S)))
->->-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
->->Cycle:
->->-> Pairs:
 MAX(N(L(x:S),N(y:S,z:S))) -> MAX(N(y:S,z:S))
->->-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pairs Processor:
-> Pairs:
 MAX(N(L(s(x:S)),L(s(y:S)))) -> MAX(N(L(x:S),L(y:S)))
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[max](X) = 0
[0] = 0
[L](X) = 2.X
[N](X1,X2) = 2.X1 + 2.X2
[fSNonEmpty] = 0
[s](X) = 2.X + 2
[MAX](X) = 2.X

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 MAX(N(L(x:S),N(y:S,z:S))) -> MAX(N(y:S,z:S))
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
->Projection:
 pi(MAX) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 max(L(x:S)) -> x:S
 max(N(L(0),L(y:S))) -> y:S
 max(N(L(s(x:S)),L(s(y:S)))) -> s(max(N(L(x:S),L(y:S))))
 max(N(L(x:S),N(y:S,z:S))) -> max(N(L(x:S),L(max(N(y:S,z:S)))))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.