details

property	value
status	complete
benchmark	ExAppendixB_AEL03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.023028 seconds
cpu usage	0.023632
user time	0.011275
system time	0.012357
max virtual memory	113188.0
max residence set size	6668.0

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) (cons2 2) (negrecip 1) (posrecip 1) (rcons 1 2) (rnil) (s 1) ) (RULES 2ndsneg(0,Z) -> rnil 2ndsneg(s(N),cons(X,Z)) -> 2ndsneg(s(N),cons2(X,Z)) 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) 2ndspos(0,Z) -> rnil 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,Z)) 2ndspos(s(N),cons2(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,Z)) -> 2ndsneg(s(N),cons2(X,Z)) 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) 2ndspos(0,Z) -> rnil 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,Z)) 2ndspos(s(N),cons2(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,Z)) -> 2NDSNEG(s(N),cons2(X,Z)) 2NDSNEG(s(N),cons(X,Z)) -> Z 2NDSNEG(s(N),cons2(X,cons(Y,Z))) -> 2NDSPOS(N,Z) 2NDSNEG(s(N),cons2(X,cons(Y,Z))) -> Z 2NDSPOS(s(N),cons(X,Z)) -> 2NDSPOS(s(N),cons2(X,Z)) 2NDSPOS(s(N),cons(X,Z)) -> Z 2NDSPOS(s(N),cons2(X,cons(Y,Z))) -> 2NDSNEG(N,Z) 2NDSPOS(s(N),cons2(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,Z)) -> 2ndsneg(s(N),cons2(X,Z)) 2ndsneg(s(N),cons2(X,cons(Y,Z))) -> rcons(negrecip(Y),2ndspos(N,Z)) 2ndspos(0,Z) -> rnil 2ndspos(s(N),cons(X,Z)) -> 2ndspos(s(N),cons2(X,Z)) 2ndspos(s(N),cons2(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,Z)) -> 2NDSNEG(s(N),cons2(X,Z)) 2NDSNEG(s(N),cons(X,Z)) -> Z 2NDSNEG(s(N),cons2(X,cons(Y,Z))) -> 2NDSPOS(N,Z) popout

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actions

all output return to TRS Contextsensitive