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TRS Contextsensitive pair #487092480
details
property
value
status
complete
benchmark
Ex1_2_AEL03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.0203319 seconds
cpu usage
0.02086
user time
0.012159
system time
0.008701
max virtual memory
113188.0
max residence set size
6556.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR N X Y Z) (STRATEGY CONTEXTSENSITIVE (2ndsneg 1 2) (2ndspos 1 2) (from 1) (pi 1) (plus 1 2) (square 1) (times 1 2) (0) (cons 1) (negrecip 1) (posrecip 1) (rcons 1 2) (rnil) (s 1) ) (RULES 2ndsneg(0,Z) -> rnil 2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) 2ndspos(0,Z) -> rnil 2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z)) from(X) -> cons(X,from(s(X))) pi(X) -> 2ndspos(X,from(0)) plus(0,Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) square(X) -> times(X,X) times(0,Y) -> 0 times(s(X),Y) -> plus(Y,times(X,Y)) ) Problem 1: Innermost Equivalent Processor: -> Rules: 2ndsneg(0,Z) -> rnil 2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) 2ndspos(0,Z) -> rnil 2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z)) from(X) -> cons(X,from(s(X))) pi(X) -> 2ndspos(X,from(0)) plus(0,Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) square(X) -> times(X,X) times(0,Y) -> 0 times(s(X),Y) -> plus(Y,times(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: 2NDSNEG(s(N),cons(X,cons(Y,Z))) -> 2NDSPOS(N,Z) 2NDSNEG(s(N),cons(X,cons(Y,Z))) -> Y 2NDSNEG(s(N),cons(X,cons(Y,Z))) -> Z 2NDSPOS(s(N),cons(X,cons(Y,Z))) -> 2NDSNEG(N,Z) 2NDSPOS(s(N),cons(X,cons(Y,Z))) -> Y 2NDSPOS(s(N),cons(X,cons(Y,Z))) -> Z PI(X) -> 2NDSPOS(X,from(0)) PI(X) -> FROM(0) PLUS(s(X),Y) -> PLUS(X,Y) SQUARE(X) -> TIMES(X,X) TIMES(s(X),Y) -> PLUS(Y,times(X,Y)) TIMES(s(X),Y) -> TIMES(X,Y) -> Rules: 2ndsneg(0,Z) -> rnil 2ndsneg(s(N),cons(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) 2ndspos(0,Z) -> rnil 2ndspos(s(N),cons(X,cons(Y,Z))) -> rcons(posrecip(Y),2ndsneg(N,Z)) from(X) -> cons(X,from(s(X))) pi(X) -> 2ndspos(X,from(0)) plus(0,Y) -> Y plus(s(X),Y) -> s(plus(X,Y)) square(X) -> times(X,X) times(0,Y) -> 0 times(s(X),Y) -> plus(Y,times(X,Y)) -> Unhiding Rules: from(s(X)) -> FROM(s(X)) Problem 1: SCC Processor: -> Pairs: 2NDSNEG(s(N),cons(X,cons(Y,Z))) -> 2NDSPOS(N,Z) 2NDSNEG(s(N),cons(X,cons(Y,Z))) -> Y 2NDSNEG(s(N),cons(X,cons(Y,Z))) -> Z 2NDSPOS(s(N),cons(X,cons(Y,Z))) -> 2NDSNEG(N,Z) 2NDSPOS(s(N),cons(X,cons(Y,Z))) -> Y 2NDSPOS(s(N),cons(X,cons(Y,Z))) -> Z PI(X) -> 2NDSPOS(X,from(0)) PI(X) -> FROM(0) PLUS(s(X),Y) -> PLUS(X,Y) SQUARE(X) -> TIMES(X,X) TIMES(s(X),Y) -> PLUS(Y,times(X,Y)) TIMES(s(X),Y) -> TIMES(X,Y)
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