/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
*(s(x),s(y)) -> s(+(+(*(x,y),x),y))
*(h,x) -> h
*(x,h) -> h
+(+(x,y),z) -> +(x,+(y,z))
+(s(x),s(y)) -> s(s(+(x,y)))
+(h,x) -> x
+(x,h) -> x
a(s(l),h,h,z) -> a(l,z,h,z)
a(h,h,h,x) -> s(x)
a(l,s(x),h,z) -> a(l,x,z,z)
a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
a(l,x,s(y),h) -> a(l,x,y,s(h))
s(h) -> 1
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(s(x),s(y)) -> *#(x,y)
 *#(s(x),s(y)) -> +#(*(x,y),x)
 *#(s(x),s(y)) -> +#(+(*(x,y),x),y)
 *#(s(x),s(y)) -> S(+(+(*(x,y),x),y))
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
 +#(s(x),s(y)) -> S(+(x,y))
 +#(s(x),s(y)) -> S(s(+(x,y)))
 A(s(l),h,h,z) -> A(l,z,h,z)
 A(h,h,h,x) -> S(x)
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
 A(l,x,s(y),h) -> S(h)
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1

Problem 1: 

SCC Processor:
-> Pairs:
 *#(s(x),s(y)) -> *#(x,y)
 *#(s(x),s(y)) -> +#(*(x,y),x)
 *#(s(x),s(y)) -> +#(+(*(x,y),x),y)
 *#(s(x),s(y)) -> S(+(+(*(x,y),x),y))
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
 +#(s(x),s(y)) -> S(+(x,y))
 +#(s(x),s(y)) -> S(s(+(x,y)))
 A(s(l),h,h,z) -> A(l,z,h,z)
 A(h,h,h,x) -> S(x)
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
 A(l,x,s(y),h) -> S(h)
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(s(l),h,h,z) -> A(l,z,h,z)
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
->->-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->->Cycle:
->->-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
->->-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->->Cycle:
->->-> Pairs:
 *#(s(x),s(y)) -> *#(x,y)
->->-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A(s(l),h,h,z) -> A(l,z,h,z)
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Projection:
 pi(A) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
->->-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A(l,s(x),h,z) -> A(l,x,z,z)
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Projection:
 pi(A) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
->->-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
 A(l,x,s(y),s(z)) -> A(l,x,y,a(l,x,s(y),z))
 A(l,x,s(y),h) -> A(l,x,y,s(h))
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Projection:
 pi(A) = 3

Problem 1.1: 

SCC Processor:
-> Pairs:
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
->->-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1

Problem 1.1: 

Subterm Processor:
-> Pairs:
 A(l,x,s(y),s(z)) -> A(l,x,s(y),z)
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Projection:
 pi(A) = 4

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(+(x,y),z) -> +#(x,+(y,z))
 +#(+(x,y),z) -> +#(y,z)
 +#(s(x),s(y)) -> +#(x,y)
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Projection:
 pi(+#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 *#(s(x),s(y)) -> *#(x,y)
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Projection:
 pi(*#) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(s(x),s(y)) -> s(+(+(*(x,y),x),y))
 *(h,x) -> h
 *(x,h) -> h
 +(+(x,y),z) -> +(x,+(y,z))
 +(s(x),s(y)) -> s(s(+(x,y)))
 +(h,x) -> x
 +(x,h) -> x
 a(s(l),h,h,z) -> a(l,z,h,z)
 a(h,h,h,x) -> s(x)
 a(l,s(x),h,z) -> a(l,x,z,z)
 a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
 a(l,x,s(y),h) -> a(l,x,y,s(h))
 s(h) -> 1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.