/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)
(STRATEGY CONTEXTSENSITIVE
(if 1)
(isZero 1)
(p 1)
(plus 1 2)
(0)
(false)
(s 1)
(true)
)
(RULES
if(false,x,y) -> y
if(true,x,y) -> x
isZero(0) -> true
isZero(s(x)) -> false
p(s(x)) -> x
plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 IF(false,x,y) -> y
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
 PLUS(x,y) -> ISZERO(x)
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> Unhiding Rules:
 s(plus(p(x),y)) -> P(x)
 s(plus(p(x),y)) -> PLUS(p(x),y)

Problem 1: 

SCC Processor:
-> Pairs:
 IF(false,x,y) -> y
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
 PLUS(x,y) -> ISZERO(x)
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> Unhiding rules:
 s(plus(p(x),y)) -> P(x)
 s(plus(p(x),y)) -> PLUS(p(x),y)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 IF(false,x,y) -> y
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
->->-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
->->-> Unhiding rules:
 s(plus(p(x),y)) -> PLUS(p(x),y)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 IF(false,x,y) -> y
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> Unhiding rules:
 s(plus(p(x),y)) -> PLUS(p(x),y)
-> Usable rules:
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[isZero](X) = 2.X
[p](X) = 1/2.X
[plus](X1,X2) = X1.X2 + X1 + 1/2
[0] = 2
[false] = 2
[s](X) = 2.X + 1
[true] = 2
[IF](X1,X2,X3) = 1/2.X1.X2 + 1/2.X1 + X3
[PLUS](X1,X2) = 2.X1.X2 + 2.X1 + 2

Problem 1: 

SCC Processor:
-> Pairs:
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> Unhiding rules:
 s(plus(p(x),y)) -> PLUS(p(x),y)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
->->-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
->->-> Unhiding rules:
 s(plus(p(x),y)) -> PLUS(p(x),y)

Problem 1: 

SubNColl Processor:
-> Pairs:
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> Unhiding rules:
 s(plus(p(x),y)) -> PLUS(p(x),y)
->Projection:
 pi(IF) = 2
 pi(PLUS) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 IF(true,x,y) -> x
 PLUS(x,y) -> IF(isZero(x),y,s(plus(p(x),y)))
-> Rules:
 if(false,x,y) -> y
 if(true,x,y) -> x
 isZero(0) -> true
 isZero(s(x)) -> false
 p(s(x)) -> x
 plus(x,y) -> if(isZero(x),y,s(plus(p(x),y)))
-> Unhiding rules:
 Empty
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.