/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 X1:S X2:S X3:S X4:S Y:S Z:S)
(RULES
plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(s(s(Y:S)),Z:S)
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(s(s(Y:S)),Z:S)
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(s(s(Y:S)),Z:S)
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
->->-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(s(s(Y:S)),Z:S)
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
-> Usable rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[plus](X1,X2) = 2.X1 + X2 + 2
[s](X) = X
[PLUS](X1,X2) = 2.X1 + X2

Problem 1: 

SCC Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
->->-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X2:S,X4:S)
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
-> Usable rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[plus](X1,X2) = 2.X1 + X2 + 2
[s](X) = X
[PLUS](X1,X2) = 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
->->-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X3:S,plus(X2:S,X4:S))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
-> Usable rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[plus](X1,X2) = 2.X1 + X2 + 2
[s](X) = X
[PLUS](X1,X2) = 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->->-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))

Problem 1: 

Subterm Processor:
-> Pairs:
 PLUS(s(X:S),plus(Y:S,Z:S)) -> PLUS(X:S,plus(s(s(Y:S)),Z:S))
 PLUS(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> PLUS(X1:S,plus(X3:S,plus(X2:S,X4:S)))
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Projection:
 pi(PLUS) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 plus(s(X:S),plus(Y:S,Z:S)) -> plus(X:S,plus(s(s(Y:S)),Z:S))
 plus(s(X1:S),plus(X2:S,plus(X3:S,X4:S))) -> plus(X1:S,plus(X3:S,plus(X2:S,X4:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.