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TRS Innermost pair #487092942
details
property
value
status
complete
benchmark
#4.30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
204.369 seconds
cpu usage
203.733
user time
184.338
system time
19.395
max virtual memory
709924.0
max residence set size
6608.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES if_quot(ffalse,x:S,y:S) -> 0 if_quot(ttrue,x:S,y:S) -> s(quot(minus(x:S,y:S),y:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quot(x:S,s(y:S)) -> if_quot(le(s(y:S),x:S),x:S,s(y:S)) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: IF_QUOT(ttrue,x:S,y:S) -> MINUS(x:S,y:S) IF_QUOT(ttrue,x:S,y:S) -> QUOT(minus(x:S,y:S),y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(x:S,s(y:S)) -> IF_QUOT(le(s(y:S),x:S),x:S,s(y:S)) QUOT(x:S,s(y:S)) -> LE(s(y:S),x:S) -> Rules: if_quot(ffalse,x:S,y:S) -> 0 if_quot(ttrue,x:S,y:S) -> s(quot(minus(x:S,y:S),y:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quot(x:S,s(y:S)) -> if_quot(le(s(y:S),x:S),x:S,s(y:S)) Problem 1: SCC Processor: -> Pairs: IF_QUOT(ttrue,x:S,y:S) -> MINUS(x:S,y:S) IF_QUOT(ttrue,x:S,y:S) -> QUOT(minus(x:S,y:S),y:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) QUOT(x:S,s(y:S)) -> IF_QUOT(le(s(y:S),x:S),x:S,s(y:S)) QUOT(x:S,s(y:S)) -> LE(s(y:S),x:S) -> Rules: if_quot(ffalse,x:S,y:S) -> 0 if_quot(ttrue,x:S,y:S) -> s(quot(minus(x:S,y:S),y:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quot(x:S,s(y:S)) -> if_quot(le(s(y:S),x:S),x:S,s(y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y:S) ->->-> Rules: if_quot(ffalse,x:S,y:S) -> 0 if_quot(ttrue,x:S,y:S) -> s(quot(minus(x:S,y:S),y:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quot(x:S,s(y:S)) -> if_quot(le(s(y:S),x:S),x:S,s(y:S)) ->->Cycle: ->->-> Pairs: LE(s(x:S),s(y:S)) -> LE(x:S,y:S) ->->-> Rules: if_quot(ffalse,x:S,y:S) -> 0 if_quot(ttrue,x:S,y:S) -> s(quot(minus(x:S,y:S),y:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quot(x:S,s(y:S)) -> if_quot(le(s(y:S),x:S),x:S,s(y:S)) ->->Cycle: ->->-> Pairs: IF_QUOT(ttrue,x:S,y:S) -> QUOT(minus(x:S,y:S),y:S) QUOT(x:S,s(y:S)) -> IF_QUOT(le(s(y:S),x:S),x:S,s(y:S)) ->->-> Rules: if_quot(ffalse,x:S,y:S) -> 0 if_quot(ttrue,x:S,y:S) -> s(quot(minus(x:S,y:S),y:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) minus(x:S,0) -> x:S quot(x:S,s(y:S)) -> if_quot(le(s(y:S),x:S),x:S,s(y:S)) The problem is decomposed in 3 subproblems. Problem 1.1:
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