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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 PLUS(s(X),plus(Y,Z)) -> PLUS(s(s(Y)),Z)
 PLUS(s(X),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X2,X4)
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
-> Usable rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
->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),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X2,X4)
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X2,X4)
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
->->-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 PLUS(s(X),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X2,X4)
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
-> Usable rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
->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),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
->->-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 PLUS(s(X),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X3,plus(X2,X4))
-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
-> Usable rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
->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),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X),plus(Y,Z)) -> PLUS(X,plus(s(s(Y)),Z))
 PLUS(s(X1),plus(X2,plus(X3,X4))) -> PLUS(X1,plus(X3,plus(X2,X4)))
->->-> Rules:
 plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
 plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))

Problem 1: 

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

Problem 1: 

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

The problem is finite.