/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
div(0,y:S) -> 0
div(x:S,y:S) -> quot(x:S,y:S,y:S)
quot(0,s(y:S),z:S) -> 0
quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
->->-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))

Problem 1: 

Subterm Processor:
-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))
->Projection:
 pi(DIV) = 1
 pi(QUOT) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
->->-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 DIV(x:S,y:S) -> QUOT(x:S,y:S,y:S)
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0] = 2
[s](X) = 0
[DIV](X1,X2) = 2.X1 + 2.X2 + 2
[QUOT](X1,X2,X3) = 2.X1 + X2 + X3

Problem 1: 

SCC Processor:
-> Pairs:
 QUOT(x:S,0,s(z:S)) -> DIV(x:S,s(z:S))
-> Rules:
 div(0,y:S) -> 0
 div(x:S,y:S) -> quot(x:S,y:S,y:S)
 quot(0,s(y:S),z:S) -> 0
 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S)
 quot(x:S,0,s(z:S)) -> s(div(x:S,s(z:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.