/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 x y)
(RULES
*(x,0) -> 0
*(x,s(y)) -> +(*(x,y),x)
+(x,0) -> x
+(x,s(y)) -> s(+(x,y))
1 -> s(0)
fac(0) -> 1
fac(0) -> s(0)
fac(s(x)) -> *(s(x),fac(x))
floop(0,y) -> y
floop(s(x),y) -> floop(x,*(s(x),y))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(x,s(y)) -> *#(x,y)
 *#(x,s(y)) -> +#(*(x,y),x)
 +#(x,s(y)) -> +#(x,y)
 FAC(0) -> 1#
 FAC(s(x)) -> *#(s(x),fac(x))
 FAC(s(x)) -> FAC(x)
 FLOOP(s(x),y) -> *#(s(x),y)
 FLOOP(s(x),y) -> FLOOP(x,*(s(x),y))
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))

Problem 1: 

SCC Processor:
-> Pairs:
 *#(x,s(y)) -> *#(x,y)
 *#(x,s(y)) -> +#(*(x,y),x)
 +#(x,s(y)) -> +#(x,y)
 FAC(0) -> 1#
 FAC(s(x)) -> *#(s(x),fac(x))
 FAC(s(x)) -> FAC(x)
 FLOOP(s(x),y) -> *#(s(x),y)
 FLOOP(s(x),y) -> FLOOP(x,*(s(x),y))
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x,s(y)) -> +#(x,y)
->->-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->->Cycle:
->->-> Pairs:
 *#(x,s(y)) -> *#(x,y)
->->-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->->Cycle:
->->-> Pairs:
 FAC(s(x)) -> FAC(x)
->->-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->->Cycle:
->->-> Pairs:
 FLOOP(s(x),y) -> FLOOP(x,*(s(x),y))
->->-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))


The problem is decomposed in 4 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 +#(x,s(y)) -> +#(x,y)
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Projection:
 pi(+#) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 *#(x,s(y)) -> *#(x,y)
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Projection:
 pi(*#) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 FAC(s(x)) -> FAC(x)
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Projection:
 pi(FAC) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 FLOOP(s(x),y) -> FLOOP(x,*(s(x),y))
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Projection:
 pi(FLOOP) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(x,0) -> 0
 *(x,s(y)) -> +(*(x,y),x)
 +(x,0) -> x
 +(x,s(y)) -> s(+(x,y))
 1 -> s(0)
 fac(0) -> 1
 fac(0) -> s(0)
 fac(s(x)) -> *(s(x),fac(x))
 floop(0,y) -> y
 floop(s(x),y) -> floop(x,*(s(x),y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.