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


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


YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.