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TRS Standard pair #487070654
details
property
value
status
complete
benchmark
Ex1_2_AEL03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0256069 seconds
cpu usage
0.026144
user time
0.011007
system time
0.015137
max virtual memory
113188.0
max residence set size
7880.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S N:S X:S X1:S X2:S Y:S Z:S) (RULES 2ndsneg(0,Z:S) -> rnil 2ndsneg(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> rcons(negrecip(activate(Y:S)),2ndspos(N:S,activate(Z:S))) 2ndspos(0,Z:S) -> rnil 2ndspos(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> rcons(posrecip(activate(Y:S)),2ndsneg(N:S,activate(Z:S))) activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S) activate(n__from(X:S)) -> from(X:S) activate(X:S) -> X:S cons(X1:S,X2:S) -> n__cons(X1:S,X2:S) from(X:S) -> cons(X:S,n__from(s(X:S))) from(X:S) -> n__from(X:S) pi(X:S) -> 2ndspos(X:S,from(0)) plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) square(X:S) -> times(X:S,X:S) times(0,Y:S) -> 0 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: 2NDSNEG(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> 2NDSPOS(N:S,activate(Z:S)) 2NDSNEG(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Y:S) 2NDSNEG(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Z:S) 2NDSPOS(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> 2NDSNEG(N:S,activate(Z:S)) 2NDSPOS(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Y:S) 2NDSPOS(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Z:S) ACTIVATE(n__cons(X1:S,X2:S)) -> CONS(X1:S,X2:S) ACTIVATE(n__from(X:S)) -> FROM(X:S) FROM(X:S) -> CONS(X:S,n__from(s(X:S))) PI(X:S) -> 2NDSPOS(X:S,from(0)) PI(X:S) -> FROM(0) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) SQUARE(X:S) -> TIMES(X:S,X:S) TIMES(s(X:S),Y:S) -> PLUS(Y:S,times(X:S,Y:S)) TIMES(s(X:S),Y:S) -> TIMES(X:S,Y:S) -> Rules: 2ndsneg(0,Z:S) -> rnil 2ndsneg(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> rcons(negrecip(activate(Y:S)),2ndspos(N:S,activate(Z:S))) 2ndspos(0,Z:S) -> rnil 2ndspos(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> rcons(posrecip(activate(Y:S)),2ndsneg(N:S,activate(Z:S))) activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S) activate(n__from(X:S)) -> from(X:S) activate(X:S) -> X:S cons(X1:S,X2:S) -> n__cons(X1:S,X2:S) from(X:S) -> cons(X:S,n__from(s(X:S))) from(X:S) -> n__from(X:S) pi(X:S) -> 2ndspos(X:S,from(0)) plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) square(X:S) -> times(X:S,X:S) times(0,Y:S) -> 0 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) Problem 1: SCC Processor: -> Pairs: 2NDSNEG(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> 2NDSPOS(N:S,activate(Z:S)) 2NDSNEG(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Y:S) 2NDSNEG(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Z:S) 2NDSPOS(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> 2NDSNEG(N:S,activate(Z:S)) 2NDSPOS(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Y:S) 2NDSPOS(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> ACTIVATE(Z:S) ACTIVATE(n__cons(X1:S,X2:S)) -> CONS(X1:S,X2:S) ACTIVATE(n__from(X:S)) -> FROM(X:S) FROM(X:S) -> CONS(X:S,n__from(s(X:S))) PI(X:S) -> 2NDSPOS(X:S,from(0)) PI(X:S) -> FROM(0) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) SQUARE(X:S) -> TIMES(X:S,X:S) TIMES(s(X:S),Y:S) -> PLUS(Y:S,times(X:S,Y:S)) TIMES(s(X:S),Y:S) -> TIMES(X:S,Y:S) -> Rules: 2ndsneg(0,Z:S) -> rnil 2ndsneg(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> rcons(negrecip(activate(Y:S)),2ndspos(N:S,activate(Z:S))) 2ndspos(0,Z:S) -> rnil 2ndspos(s(N:S),cons(X:S,n__cons(Y:S,Z:S))) -> rcons(posrecip(activate(Y:S)),2ndsneg(N:S,activate(Z:S))) activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S) activate(n__from(X:S)) -> from(X:S) activate(X:S) -> X:S cons(X1:S,X2:S) -> n__cons(X1:S,X2:S) from(X:S) -> cons(X:S,n__from(s(X:S))) from(X:S) -> n__from(X:S) pi(X:S) -> 2ndspos(X:S,from(0)) plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) square(X:S) -> times(X:S,X:S) times(0,Y:S) -> 0 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs:
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