/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
*(0,y) -> 0
*(s(x),y) -> +(*(x,y),y)
+(x,0) -> x
+(x,s(y)) -> s(+(x,y))
fact(0) -> s(0)
fact(s(x)) -> *(s(x),fact(p(s(x))))
p(s(x)) -> x
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(s(x),y) -> *#(x,y)
 *#(s(x),y) -> +#(*(x,y),y)
 +#(x,s(y)) -> +#(x,y)
 FACT(s(x)) -> *#(s(x),fact(p(s(x))))
 FACT(s(x)) -> FACT(p(s(x)))
 FACT(s(x)) -> P(s(x))
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 *#(s(x),y) -> *#(x,y)
 *#(s(x),y) -> +#(*(x,y),y)
 +#(x,s(y)) -> +#(x,y)
 FACT(s(x)) -> *#(s(x),fact(p(s(x))))
 FACT(s(x)) -> FACT(p(s(x)))
 FACT(s(x)) -> P(s(x))
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x,s(y)) -> +#(x,y)
->->-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->->Cycle:
->->-> Pairs:
 *#(s(x),y) -> *#(x,y)
->->-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->->Cycle:
->->-> Pairs:
 FACT(s(x)) -> FACT(p(s(x)))
->->-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 +#(x,s(y)) -> +#(x,y)
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->Projection:
 pi(+#) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 *#(s(x),y) -> *#(x,y)
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->Projection:
 pi(*#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Reduction Pairs Processor:
-> Pairs:
 FACT(s(x)) -> FACT(p(s(x)))
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
-> Usable rules:
 p(s(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X) = 1/2.X
[s](X) = 2.X + 1/2
[FACT](X) = 2.X

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(*(x,y),y)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 fact(0) -> s(0)
 fact(s(x)) -> *(s(x),fact(p(s(x))))
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.