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TRS Contextsensitive pair #487092548
details
property
value
status
complete
benchmark
Ex1_Luc04b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.028447 seconds
cpu usage
0.028983
user time
0.010454
system time
0.018529
max virtual memory
113188.0
max residence set size
4936.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR X XS) (STRATEGY CONTEXTSENSITIVE (head 1) (incr 1) (nats) (odds) (pairs) (tail 1) (0) (cons 1) (s 1) ) (RULES head(cons(X,XS)) -> X incr(cons(X,XS)) -> cons(s(X),incr(XS)) nats -> cons(0,incr(nats)) odds -> incr(pairs) pairs -> cons(0,incr(odds)) tail(cons(X,XS)) -> XS ) Problem 1: Innermost Equivalent Processor: -> Rules: head(cons(X,XS)) -> X incr(cons(X,XS)) -> cons(s(X),incr(XS)) nats -> cons(0,incr(nats)) odds -> incr(pairs) pairs -> cons(0,incr(odds)) tail(cons(X,XS)) -> XS -> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination. Problem 1: Dependency Pairs Processor: -> Pairs: ODDS -> INCR(pairs) ODDS -> PAIRS TAIL(cons(X,XS)) -> XS -> Rules: head(cons(X,XS)) -> X incr(cons(X,XS)) -> cons(s(X),incr(XS)) nats -> cons(0,incr(nats)) odds -> incr(pairs) pairs -> cons(0,incr(odds)) tail(cons(X,XS)) -> XS -> Unhiding Rules: incr(nats) -> INCR(nats) incr(nats) -> NATS incr(odds) -> INCR(odds) incr(odds) -> ODDS incr(XS) -> INCR(XS) incr(x2) -> x2 Problem 1: SCC Processor: -> Pairs: ODDS -> INCR(pairs) ODDS -> PAIRS TAIL(cons(X,XS)) -> XS -> Rules: head(cons(X,XS)) -> X incr(cons(X,XS)) -> cons(s(X),incr(XS)) nats -> cons(0,incr(nats)) odds -> incr(pairs) pairs -> cons(0,incr(odds)) tail(cons(X,XS)) -> XS -> Unhiding rules: incr(nats) -> INCR(nats) incr(nats) -> NATS incr(odds) -> INCR(odds) incr(odds) -> ODDS incr(XS) -> INCR(XS) incr(x2) -> x2 ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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