Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487067439
details
property
value
status
complete
benchmark
#3.55.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.112591 seconds
cpu usage
0.110042
user time
0.066401
system time
0.043641
max virtual memory
113188.0
max residence set size
9368.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S m:S n:S x:S y:S) (RULES app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S high(n:S,add(m:S,x:S)) -> if_high(le(m:S,n:S),n:S,add(m:S,x:S)) high(n:S,nil) -> nil if_high(ffalse,n:S,add(m:S,x:S)) -> add(m:S,high(n:S,x:S)) if_high(ttrue,n:S,add(m:S,x:S)) -> high(n:S,x:S) if_low(ffalse,n:S,add(m:S,x:S)) -> low(n:S,x:S) if_low(ttrue,n:S,add(m:S,x:S)) -> add(m:S,low(n:S,x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) low(n:S,add(m:S,x:S)) -> if_low(le(m:S,n:S),n:S,add(m:S,x:S)) low(n:S,nil) -> nil minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quicksort(add(n:S,x:S)) -> app(quicksort(low(n:S,x:S)),add(n:S,quicksort(high(n:S,x:S)))) quicksort(nil) -> nil quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S high(n:S,add(m:S,x:S)) -> if_high(le(m:S,n:S),n:S,add(m:S,x:S)) high(n:S,nil) -> nil if_high(ffalse,n:S,add(m:S,x:S)) -> add(m:S,high(n:S,x:S)) if_high(ttrue,n:S,add(m:S,x:S)) -> high(n:S,x:S) if_low(ffalse,n:S,add(m:S,x:S)) -> low(n:S,x:S) if_low(ttrue,n:S,add(m:S,x:S)) -> add(m:S,low(n:S,x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) low(n:S,add(m:S,x:S)) -> if_low(le(m:S,n:S),n:S,add(m:S,x:S)) low(n:S,nil) -> nil minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quicksort(add(n:S,x:S)) -> app(quicksort(low(n:S,x:S)),add(n:S,quicksort(high(n:S,x:S)))) quicksort(nil) -> nil quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(add(n:S,x:S),y:S) -> APP(x:S,y:S) HIGH(n:S,add(m:S,x:S)) -> IF_HIGH(le(m:S,n:S),n:S,add(m:S,x:S)) HIGH(n:S,add(m:S,x:S)) -> LE(m:S,n:S) IF_HIGH(ffalse,n:S,add(m:S,x:S)) -> HIGH(n:S,x:S) IF_HIGH(ttrue,n:S,add(m:S,x:S)) -> HIGH(n:S,x:S) IF_LOW(ffalse,n:S,add(m:S,x:S)) -> LOW(n:S,x:S) IF_LOW(ttrue,n:S,add(m:S,x:S)) -> LOW(n:S,x:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) LOW(n:S,add(m:S,x:S)) -> IF_LOW(le(m:S,n:S),n:S,add(m:S,x:S)) LOW(n:S,add(m:S,x:S)) -> LE(m:S,n:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUICKSORT(add(n:S,x:S)) -> APP(quicksort(low(n:S,x:S)),add(n:S,quicksort(high(n:S,x:S)))) QUICKSORT(add(n:S,x:S)) -> HIGH(n:S,x:S) QUICKSORT(add(n:S,x:S)) -> LOW(n:S,x:S) QUICKSORT(add(n:S,x:S)) -> QUICKSORT(high(n:S,x:S)) QUICKSORT(add(n:S,x:S)) -> QUICKSORT(low(n:S,x:S)) QUOT(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(s(x:S),s(y:S)) -> QUOT(minus(x:S,y:S),s(y:S)) -> Rules: app(add(n:S,x:S),y:S) -> add(n:S,app(x:S,y:S)) app(nil,y:S) -> y:S high(n:S,add(m:S,x:S)) -> if_high(le(m:S,n:S),n:S,add(m:S,x:S)) high(n:S,nil) -> nil if_high(ffalse,n:S,add(m:S,x:S)) -> add(m:S,high(n:S,x:S)) if_high(ttrue,n:S,add(m:S,x:S)) -> high(n:S,x:S) if_low(ffalse,n:S,add(m:S,x:S)) -> low(n:S,x:S) if_low(ttrue,n:S,add(m:S,x:S)) -> add(m:S,low(n:S,x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) low(n:S,add(m:S,x:S)) -> if_low(le(m:S,n:S),n:S,add(m:S,x:S)) low(n:S,nil) -> nil minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quicksort(add(n:S,x:S)) -> app(quicksort(low(n:S,x:S)),add(n:S,quicksort(high(n:S,x:S)))) quicksort(nil) -> nil quot(0,s(y:S)) -> 0 quot(s(x:S),s(y:S)) -> s(quot(minus(x:S,y:S),s(y:S))) Problem 1: SCC Processor: -> Pairs:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard