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TRS Innermost pair #487093618
details
property
value
status
complete
benchmark
wiehe14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.511142 seconds
cpu usage
0.504694
user time
0.387023
system time
0.117671
max virtual memory
113188.0
max residence set size
9300.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) gt(s(x:S),s(y:S)) -> gt(x:S,y:S) gt(s(x:S),zero) -> ttrue gt(zero,y:S) -> ffalse half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) id(x:S) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) not(x:S) -> if(x:S,ffalse,ttrue) plus(id(x:S),s(y:S)) -> s(plus(x:S,if(gt(s(y:S),y:S),y:S,s(y:S)))) plus(s(x:S),s(y:S)) -> s(s(plus(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))))) plus(s(x:S),x:S) -> plus(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) plus(zero,y:S) -> y:S times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: EVEN(s(s(x:S))) -> EVEN(x:S) GT(s(x:S),s(y:S)) -> GT(x:S,y:S) HALF(s(s(x:S))) -> HALF(x:S) IF_TIMES(ffalse,s(x:S),y:S) -> PLUS(y:S,times(x:S,y:S)) IF_TIMES(ffalse,s(x:S),y:S) -> TIMES(x:S,y:S) IF_TIMES(ttrue,s(x:S),y:S) -> HALF(s(x:S)) IF_TIMES(ttrue,s(x:S),y:S) -> PLUS(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) IF_TIMES(ttrue,s(x:S),y:S) -> TIMES(half(s(x:S)),y:S) NOT(x:S) -> IF(x:S,ffalse,ttrue) PLUS(s(x:S),s(y:S)) -> GT(x:S,y:S) PLUS(s(x:S),s(y:S)) -> ID(x:S) PLUS(s(x:S),s(y:S)) -> ID(y:S) PLUS(s(x:S),s(y:S)) -> IF(gt(x:S,y:S),x:S,y:S) PLUS(s(x:S),s(y:S)) -> IF(not(gt(x:S,y:S)),id(x:S),id(y:S)) PLUS(s(x:S),s(y:S)) -> NOT(gt(x:S,y:S)) PLUS(s(x:S),s(y:S)) -> PLUS(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))) PLUS(s(x:S),x:S) -> GT(x:S,x:S) PLUS(s(x:S),x:S) -> ID(x:S) PLUS(s(x:S),x:S) -> IF(gt(x:S,x:S),id(x:S),id(x:S)) PLUS(s(x:S),x:S) -> PLUS(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) TIMES(s(x:S),y:S) -> EVEN(s(x:S)) TIMES(s(x:S),y:S) -> IF_TIMES(even(s(x:S)),s(x:S),y:S) -> Rules: even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) gt(s(x:S),s(y:S)) -> gt(x:S,y:S) gt(s(x:S),zero) -> ttrue gt(zero,y:S) -> ffalse half(0) -> 0 half(s(s(x:S))) -> s(half(x:S)) id(x:S) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S if_times(ffalse,s(x:S),y:S) -> plus(y:S,times(x:S,y:S)) if_times(ttrue,s(x:S),y:S) -> plus(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) not(x:S) -> if(x:S,ffalse,ttrue) plus(id(x:S),s(y:S)) -> s(plus(x:S,if(gt(s(y:S),y:S),y:S,s(y:S)))) plus(s(x:S),s(y:S)) -> s(s(plus(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))))) plus(s(x:S),x:S) -> plus(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) plus(zero,y:S) -> y:S times(0,y:S) -> 0 times(s(x:S),y:S) -> if_times(even(s(x:S)),s(x:S),y:S) Problem 1: SCC Processor: -> Pairs: EVEN(s(s(x:S))) -> EVEN(x:S) GT(s(x:S),s(y:S)) -> GT(x:S,y:S) HALF(s(s(x:S))) -> HALF(x:S) IF_TIMES(ffalse,s(x:S),y:S) -> PLUS(y:S,times(x:S,y:S)) IF_TIMES(ffalse,s(x:S),y:S) -> TIMES(x:S,y:S) IF_TIMES(ttrue,s(x:S),y:S) -> HALF(s(x:S)) IF_TIMES(ttrue,s(x:S),y:S) -> PLUS(times(half(s(x:S)),y:S),times(half(s(x:S)),y:S)) IF_TIMES(ttrue,s(x:S),y:S) -> TIMES(half(s(x:S)),y:S) NOT(x:S) -> IF(x:S,ffalse,ttrue) PLUS(s(x:S),s(y:S)) -> GT(x:S,y:S) PLUS(s(x:S),s(y:S)) -> ID(x:S) PLUS(s(x:S),s(y:S)) -> ID(y:S) PLUS(s(x:S),s(y:S)) -> IF(gt(x:S,y:S),x:S,y:S) PLUS(s(x:S),s(y:S)) -> IF(not(gt(x:S,y:S)),id(x:S),id(y:S)) PLUS(s(x:S),s(y:S)) -> NOT(gt(x:S,y:S)) PLUS(s(x:S),s(y:S)) -> PLUS(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))) PLUS(s(x:S),x:S) -> GT(x:S,x:S) PLUS(s(x:S),x:S) -> ID(x:S) PLUS(s(x:S),x:S) -> IF(gt(x:S,x:S),id(x:S),id(x:S))
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