/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

(VAR x y)
(RULES
*(0,y) -> 0
*(s(x),y) -> +(y,*(x,y))
-(0,y) -> 0
-(s(x),s(y)) -> -(x,y)
-(x,0) -> x
exp(x,0) -> s(0)
exp(x,s(y)) -> *(x,exp(x,y))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))
-> 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),s(y)) -> -#(x,y)
 EXP(x,s(y)) -> *#(x,exp(x,y))
 EXP(x,s(y)) -> EXP(x,y)
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))

Problem 1: 

SCC Processor:
-> Pairs:
 *#(s(x),y) -> *#(x,y)
 -#(s(x),s(y)) -> -#(x,y)
 EXP(x,s(y)) -> *#(x,exp(x,y))
 EXP(x,s(y)) -> EXP(x,y)
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 -#(s(x),s(y)) -> -#(x,y)
->->-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))
->->Cycle:
->->-> Pairs:
 *#(s(x),y) -> *#(x,y)
->->-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))
->->Cycle:
->->-> Pairs:
 EXP(x,s(y)) -> EXP(x,y)
->->-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))


The problem is decomposed in 3 subproblems.

Problem 1.1: 

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

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(0,y) -> 0
 *(s(x),y) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))
->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) -> +(y,*(x,y))
 -(0,y) -> 0
 -(s(x),s(y)) -> -(x,y)
 -(x,0) -> x
 exp(x,0) -> s(0)
 exp(x,s(y)) -> *(x,exp(x,y))
->Projection:
 pi(*#) = 1

Problem 1.2: 

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

The problem is finite.

Problem 1.3: 

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

Problem 1.3: 

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

The problem is finite.