/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
div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
div(X:S,e) -> i(X:S)
i(div(X:S,Y:S)) -> div(Y:S,X:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(i(X:S),Z:S)
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(i(X:S),Z:S)
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(i(X:S),Z:S)
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
->->-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(i(X:S),Z:S)
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)
-> Usable rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[div](X1,X2) = 2.X1 + X2 + 2
[i](X) = 2.X + 1
[e] = 0
[DIV](X1,X2) = 2.X1
[I](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
->->-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 DIV(div(X:S,Y:S),Z:S) -> DIV(Y:S,div(i(X:S),Z:S))
 DIV(div(X:S,Y:S),Z:S) -> I(X:S)
 DIV(X:S,e) -> I(X:S)
 I(div(X:S,Y:S)) -> DIV(Y:S,X:S)
-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)
->Projection:
 pi(DIV) = 1
 pi(I) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 DIV(X:S,e) -> I(X:S)
-> Rules:
 div(div(X:S,Y:S),Z:S) -> div(Y:S,div(i(X:S),Z:S))
 div(X:S,e) -> i(X:S)
 i(div(X:S,Y:S)) -> div(Y:S,X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.