TRS Condi 20667 pair #381733077

details

property	value
status	complete
benchmark	307.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n016.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.0164020061493 seconds
cpu usage	0.013000447
max memory	1490944.0

stage attributes

key	value
output-size	3384
starexec-result	YES

output

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


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


YES

Problem 1: 

(VAR W X Y Z)
(RULES
fib(0) -> pair(s(0),0)
fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
plus(0,X) -> X
plus(s(X),Y) -> plus(X,s(Y))
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 fib(0) -> pair(s(0),0)
 fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
 plus(0,X) -> X
 plus(s(X),Y) -> plus(X,s(Y))
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 PLUS(s(X),Y) -> PLUS(X,s(Y))
-> QPairs:
 Empty
-> Rules:
 fib(0) -> pair(s(0),0)
 fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
 plus(0,X) -> X
 plus(s(X),Y) -> plus(X,s(Y))

Conditional Termination Problem 2:
-> Pairs:
 FIB(s(X)) -> FIB(X)
 FIB(s(X)) -> PLUS(Y,Z) | fib(X) -> pair(Y,Z)
-> QPairs:
 PLUS(s(X),Y) -> PLUS(X,s(Y))
-> Rules:
 fib(0) -> pair(s(0),0)
 fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
 plus(0,X) -> X
 plus(s(X),Y) -> plus(X,s(Y))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 PLUS(s(X),Y) -> PLUS(X,s(Y))
-> QPairs:
 Empty
-> Rules:
 fib(0) -> pair(s(0),0)
 fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
 plus(0,X) -> X
 plus(s(X),Y) -> plus(X,s(Y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(X),Y) -> PLUS(X,s(Y))
->->-> Rules:
 fib(0) -> pair(s(0),0)
 fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
 plus(0,X) -> X
 plus(s(X),Y) -> plus(X,s(Y))

Problem 1.1: 

Conditional Subterm Processor:
-> Pairs:
 PLUS(s(X),Y) -> PLUS(X,s(Y))
-> QPairs:
 Empty
-> Rules:
 fib(0) -> pair(s(0),0)
 fib(s(X)) -> pair(W,Y) | fib(X) -> pair(Y,Z), plus(Y,Z) -> W
 plus(0,X) -> X
 plus(s(X),Y) -> plus(X,s(Y))
->Projection:
 pi(PLUS) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:

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