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


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YES

Problem 1: 

(VAR x y)
(RULES
D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
D(+(x,y)) -> +(D(x),D(y))
D(-(x,y)) -> -(D(x),D(y))
D(constant) -> 0
D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
D(ln(x)) -> div(D(x),x)
D(minus(x)) -> minus(D(x))
D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
D(t) -> 1
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
 D(+(x,y)) -> +(D(x),D(y))
 D(-(x,y)) -> -(D(x),D(y))
 D(constant) -> 0
 D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
 D(ln(x)) -> div(D(x),x)
 D(minus(x)) -> minus(D(x))
 D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
 D(t) -> 1
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 D#(*(x,y)) -> D#(x)
 D#(*(x,y)) -> D#(y)
 D#(+(x,y)) -> D#(x)
 D#(+(x,y)) -> D#(y)
 D#(-(x,y)) -> D#(x)
 D#(-(x,y)) -> D#(y)
 D#(div(x,y)) -> D#(x)
 D#(div(x,y)) -> D#(y)
 D#(ln(x)) -> D#(x)
 D#(minus(x)) -> D#(x)
 D#(pow(x,y)) -> D#(x)
 D#(pow(x,y)) -> D#(y)
-> Rules:
 D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
 D(+(x,y)) -> +(D(x),D(y))
 D(-(x,y)) -> -(D(x),D(y))
 D(constant) -> 0
 D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
 D(ln(x)) -> div(D(x),x)
 D(minus(x)) -> minus(D(x))
 D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
 D(t) -> 1

Problem 1: 

SCC Processor:
-> Pairs:
 D#(*(x,y)) -> D#(x)
 D#(*(x,y)) -> D#(y)
 D#(+(x,y)) -> D#(x)
 D#(+(x,y)) -> D#(y)
 D#(-(x,y)) -> D#(x)
 D#(-(x,y)) -> D#(y)
 D#(div(x,y)) -> D#(x)
 D#(div(x,y)) -> D#(y)
 D#(ln(x)) -> D#(x)
 D#(minus(x)) -> D#(x)
 D#(pow(x,y)) -> D#(x)
 D#(pow(x,y)) -> D#(y)
-> Rules:
 D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
 D(+(x,y)) -> +(D(x),D(y))
 D(-(x,y)) -> -(D(x),D(y))
 D(constant) -> 0
 D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
 D(ln(x)) -> div(D(x),x)
 D(minus(x)) -> minus(D(x))
 D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
 D(t) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 D#(*(x,y)) -> D#(x)
 D#(*(x,y)) -> D#(y)
 D#(+(x,y)) -> D#(x)
 D#(+(x,y)) -> D#(y)
 D#(-(x,y)) -> D#(x)
 D#(-(x,y)) -> D#(y)
 D#(div(x,y)) -> D#(x)
 D#(div(x,y)) -> D#(y)
 D#(ln(x)) -> D#(x)
 D#(minus(x)) -> D#(x)
 D#(pow(x,y)) -> D#(x)
 D#(pow(x,y)) -> D#(y)
->->-> Rules:
 D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
 D(+(x,y)) -> +(D(x),D(y))
 D(-(x,y)) -> -(D(x),D(y))
 D(constant) -> 0
 D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
 D(ln(x)) -> div(D(x),x)
 D(minus(x)) -> minus(D(x))
 D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
 D(t) -> 1

Problem 1: 

Subterm Processor:
-> Pairs:
 D#(*(x,y)) -> D#(x)
 D#(*(x,y)) -> D#(y)
 D#(+(x,y)) -> D#(x)
 D#(+(x,y)) -> D#(y)
 D#(-(x,y)) -> D#(x)
 D#(-(x,y)) -> D#(y)
 D#(div(x,y)) -> D#(x)
 D#(div(x,y)) -> D#(y)
 D#(ln(x)) -> D#(x)
 D#(minus(x)) -> D#(x)
 D#(pow(x,y)) -> D#(x)
 D#(pow(x,y)) -> D#(y)
-> Rules:
 D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
 D(+(x,y)) -> +(D(x),D(y))
 D(-(x,y)) -> -(D(x),D(y))
 D(constant) -> 0
 D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
 D(ln(x)) -> div(D(x),x)
 D(minus(x)) -> minus(D(x))
 D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
 D(t) -> 1
->Projection:
 pi(D#) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
 D(+(x,y)) -> +(D(x),D(y))
 D(-(x,y)) -> -(D(x),D(y))
 D(constant) -> 0
 D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2)))
 D(ln(x)) -> div(D(x),x)
 D(minus(x)) -> minus(D(x))
 D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1))),D(x)),*(*(pow(x,y),ln(x)),D(y)))
 D(t) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.