Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487067504
details
property
value
status
complete
benchmark
#3.13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.112201 seconds
cpu usage
0.100055
user time
0.056598
system time
0.043457
max virtual memory
113188.0
max residence set size
9040.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S h:S i:S u:S v:S x:S y:S) (RULES eq(0,0) -> ttrue eq(0,s(x:S)) -> ffalse eq(s(x:S),0) -> ffalse eq(s(x:S),s(y:S)) -> eq(x:S,y:S) if_reach_1(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> reach(x:S,y:S,i:S,edge(u:S,v:S,h:S)) if_reach_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_2(eq(y:S,v:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) if_reach_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> or(reach(x:S,y:S,i:S,h:S),reach(v:S,y:S,union(i:S,h:S),empty)) if_reach_2(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> ttrue or(ffalse,y:S) -> y:S or(ttrue,y:S) -> ttrue reach(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_1(eq(x:S,u:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) reach(x:S,y:S,empty,h:S) -> ffalse union(edge(x:S,y:S,i:S),h:S) -> edge(x:S,y:S,union(i:S,h:S)) union(empty,h:S) -> h:S ) Problem 1: Innermost Equivalent Processor: -> Rules: eq(0,0) -> ttrue eq(0,s(x:S)) -> ffalse eq(s(x:S),0) -> ffalse eq(s(x:S),s(y:S)) -> eq(x:S,y:S) if_reach_1(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> reach(x:S,y:S,i:S,edge(u:S,v:S,h:S)) if_reach_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_2(eq(y:S,v:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) if_reach_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> or(reach(x:S,y:S,i:S,h:S),reach(v:S,y:S,union(i:S,h:S),empty)) if_reach_2(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> ttrue or(ffalse,y:S) -> y:S or(ttrue,y:S) -> ttrue reach(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_1(eq(x:S,u:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) reach(x:S,y:S,empty,h:S) -> ffalse union(edge(x:S,y:S,i:S),h:S) -> edge(x:S,y:S,union(i:S,h:S)) union(empty,h:S) -> h:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: EQ(s(x:S),s(y:S)) -> EQ(x:S,y:S) IF_REACH_1(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> REACH(x:S,y:S,i:S,edge(u:S,v:S,h:S)) IF_REACH_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> EQ(y:S,v:S) IF_REACH_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> IF_REACH_2(eq(y:S,v:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> OR(reach(x:S,y:S,i:S,h:S),reach(v:S,y:S,union(i:S,h:S),empty)) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> REACH(v:S,y:S,union(i:S,h:S),empty) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> REACH(x:S,y:S,i:S,h:S) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> UNION(i:S,h:S) REACH(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> EQ(x:S,u:S) REACH(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> IF_REACH_1(eq(x:S,u:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) UNION(edge(x:S,y:S,i:S),h:S) -> UNION(i:S,h:S) -> Rules: eq(0,0) -> ttrue eq(0,s(x:S)) -> ffalse eq(s(x:S),0) -> ffalse eq(s(x:S),s(y:S)) -> eq(x:S,y:S) if_reach_1(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> reach(x:S,y:S,i:S,edge(u:S,v:S,h:S)) if_reach_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_2(eq(y:S,v:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) if_reach_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> or(reach(x:S,y:S,i:S,h:S),reach(v:S,y:S,union(i:S,h:S),empty)) if_reach_2(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> ttrue or(ffalse,y:S) -> y:S or(ttrue,y:S) -> ttrue reach(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_1(eq(x:S,u:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) reach(x:S,y:S,empty,h:S) -> ffalse union(edge(x:S,y:S,i:S),h:S) -> edge(x:S,y:S,union(i:S,h:S)) union(empty,h:S) -> h:S Problem 1: SCC Processor: -> Pairs: EQ(s(x:S),s(y:S)) -> EQ(x:S,y:S) IF_REACH_1(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> REACH(x:S,y:S,i:S,edge(u:S,v:S,h:S)) IF_REACH_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> EQ(y:S,v:S) IF_REACH_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> IF_REACH_2(eq(y:S,v:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> OR(reach(x:S,y:S,i:S,h:S),reach(v:S,y:S,union(i:S,h:S),empty)) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> REACH(v:S,y:S,union(i:S,h:S),empty) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> REACH(x:S,y:S,i:S,h:S) IF_REACH_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> UNION(i:S,h:S) REACH(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> EQ(x:S,u:S) REACH(x:S,y:S,edge(u:S,v:S,i:S),h:S) -> IF_REACH_1(eq(x:S,u:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) UNION(edge(x:S,y:S,i:S),h:S) -> UNION(i:S,h:S) -> Rules: eq(0,0) -> ttrue eq(0,s(x:S)) -> ffalse eq(s(x:S),0) -> ffalse eq(s(x:S),s(y:S)) -> eq(x:S,y:S) if_reach_1(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> reach(x:S,y:S,i:S,edge(u:S,v:S,h:S)) if_reach_1(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> if_reach_2(eq(y:S,v:S),x:S,y:S,edge(u:S,v:S,i:S),h:S) if_reach_2(ffalse,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> or(reach(x:S,y:S,i:S,h:S),reach(v:S,y:S,union(i:S,h:S),empty)) if_reach_2(ttrue,x:S,y:S,edge(u:S,v:S,i:S),h:S) -> ttrue or(ffalse,y:S) -> y:S or(ttrue,y:S) -> ttrue
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard