/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 l x y z)
(RULES
*(*(x,y),z) -> *(x,*(y,z))
*(0,x) -> 0
*(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
*(x,0) -> 0
+(+(x,y),z) -> +(x,+(y,z))
+(0,x) -> x
+(s(x),s(y)) -> s(s(+(x,y)))
+(x,0) -> x
prod(cons(x,l)) -> *(x,prod(l))
prod(nil) -> s(0)
sum(cons(x,l)) -> +(x,sum(l))
sum(nil) -> 0
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(*(x,y),z) -> *#(x,*(y,z))
 *#(*(x,y),z) -> *#(y,z)
 *#(s(x),s(y)) -> *#(x,y)
 *#(s(x),s(y)) -> +#(*(x,y),+(x,y))
 *#(s(x),s(y)) -> +#(x,y)
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
 PROD(cons(x,l)) -> *#(x,prod(l))
 PROD(cons(x,l)) -> PROD(l)
 SUM(cons(x,l)) -> +#(x,sum(l))
 SUM(cons(x,l)) -> SUM(l)
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0

Problem 1: 

SCC Processor:
-> Pairs:
 *#(*(x,y),z) -> *#(x,*(y,z))
 *#(*(x,y),z) -> *#(y,z)
 *#(s(x),s(y)) -> *#(x,y)
 *#(s(x),s(y)) -> +#(*(x,y),+(x,y))
 *#(s(x),s(y)) -> +#(x,y)
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
 PROD(cons(x,l)) -> *#(x,prod(l))
 PROD(cons(x,l)) -> PROD(l)
 SUM(cons(x,l)) -> +#(x,sum(l))
 SUM(cons(x,l)) -> SUM(l)
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
->->-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->->Cycle:
->->-> Pairs:
 SUM(cons(x,l)) -> SUM(l)
->->-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->->Cycle:
->->-> Pairs:
 *#(*(x,y),z) -> *#(x,*(y,z))
 *#(*(x,y),z) -> *#(y,z)
 *#(s(x),s(y)) -> *#(x,y)
->->-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->->Cycle:
->->-> Pairs:
 PROD(cons(x,l)) -> PROD(l)
->->-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0


The problem is decomposed in 4 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Projection:
 pi(+#) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 SUM(cons(x,l)) -> SUM(l)
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Projection:
 pi(SUM) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 *#(*(x,y),z) -> *#(x,*(y,z))
 *#(*(x,y),z) -> *#(y,z)
 *#(s(x),s(y)) -> *#(x,y)
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Projection:
 pi(*#) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 PROD(cons(x,l)) -> PROD(l)
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Projection:
 pi(PROD) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(*(x,y),z) -> *(x,*(y,z))
 *(0,x) -> 0
 *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
 *(x,0) -> 0
 +(+(x,y),z) -> +(x,+(y,z))
 +(0,x) -> x
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(x,0) -> x
 prod(cons(x,l)) -> *(x,prod(l))
 prod(nil) -> s(0)
 sum(cons(x,l)) -> +(x,sum(l))
 sum(nil) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.