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TRS Standard pair #487067502
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
n186.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.11515 seconds
cpu usage
7.10276
user time
5.82891
system time
1.27385
max virtual memory
5867928.0
max residence set size
91484.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) or(true(),y) -> true() or(false(),y) -> y union(empty(),h) -> h union(edge(x,y,i),h) -> edge(x,y,union(i,h)) reach(x,y,empty(),h) -> false() reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(true(),x,y,edge(u,v,i),h) -> true() if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) Proof: DP Processor: DPs: eq#(s(x),s(y)) -> eq#(x,y) union#(edge(x,y,i),h) -> union#(i,h) reach#(x,y,edge(u,v,i),h) -> eq#(x,u) reach#(x,y,edge(u,v,i),h) -> if_reach_1#(eq(x,u),x,y,edge(u,v,i),h) if_reach_1#(true(),x,y,edge(u,v,i),h) -> eq#(y,v) if_reach_1#(true(),x,y,edge(u,v,i),h) -> if_reach_2#(eq(y,v),x,y,edge(u,v,i),h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> union#(i,h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(v,y,union(i,h),empty()) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> or#(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_1#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,edge(u,v,h)) TRS: eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) or(true(),y) -> true() or(false(),y) -> y union(empty(),h) -> h union(edge(x,y,i),h) -> edge(x,y,union(i,h)) reach(x,y,empty(),h) -> false() reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(true(),x,y,edge(u,v,i),h) -> true() if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) TDG Processor: DPs: eq#(s(x),s(y)) -> eq#(x,y) union#(edge(x,y,i),h) -> union#(i,h) reach#(x,y,edge(u,v,i),h) -> eq#(x,u) reach#(x,y,edge(u,v,i),h) -> if_reach_1#(eq(x,u),x,y,edge(u,v,i),h) if_reach_1#(true(),x,y,edge(u,v,i),h) -> eq#(y,v) if_reach_1#(true(),x,y,edge(u,v,i),h) -> if_reach_2#(eq(y,v),x,y,edge(u,v,i),h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> union#(i,h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(v,y,union(i,h),empty()) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> or#(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_1#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,edge(u,v,h)) TRS: eq(0(),0()) -> true() eq(0(),s(x)) -> false() eq(s(x),0()) -> false() eq(s(x),s(y)) -> eq(x,y) or(true(),y) -> true() or(false(),y) -> y union(empty(),h) -> h union(edge(x,y,i),h) -> edge(x,y,union(i,h)) reach(x,y,empty(),h) -> false() reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(true(),x,y,edge(u,v,i),h) -> true() if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) graph: if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(v,y,union(i,h),empty()) -> reach#(x,y,edge(u,v,i),h) -> if_reach_1#(eq(x,u),x,y,edge(u,v,i),h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(v,y,union(i,h),empty()) -> reach#(x,y,edge(u,v,i),h) -> eq#(x,u) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,h) -> reach#(x,y,edge(u,v,i),h) -> if_reach_1#(eq(x,u),x,y,edge(u,v,i),h) if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,h) -> reach#(x,y,edge(u,v,i),h) -> eq#(x,u) if_reach_2#(false(),x,y,edge(u,v,i),h) -> union#(i,h) -> union#(edge(x,y,i),h) -> union#(i,h) if_reach_1#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,edge(u,v,h)) -> reach#(x,y,edge(u,v,i),h) -> if_reach_1#(eq(x,u),x,y,edge(u,v,i),h) if_reach_1#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,edge(u,v,h)) -> reach#(x,y,edge(u,v,i),h) -> eq#(x,u) if_reach_1#(true(),x,y,edge(u,v,i),h) -> if_reach_2#(eq(y,v),x,y,edge(u,v,i),h) -> if_reach_2#(false(),x,y,edge(u,v,i),h) -> or#(reach(x,y,i,h),reach(v,y,union(i,h),empty())) if_reach_1#(true(),x,y,edge(u,v,i),h) -> if_reach_2#(eq(y,v),x,y,edge(u,v,i),h) -> if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(x,y,i,h) if_reach_1#(true(),x,y,edge(u,v,i),h) -> if_reach_2#(eq(y,v),x,y,edge(u,v,i),h) -> if_reach_2#(false(),x,y,edge(u,v,i),h) -> reach#(v,y,union(i,h),empty()) if_reach_1#(true(),x,y,edge(u,v,i),h) -> if_reach_2#(eq(y,v),x,y,edge(u,v,i),h) -> if_reach_2#(false(),x,y,edge(u,v,i),h) -> union#(i,h) if_reach_1#(true(),x,y,edge(u,v,i),h) -> eq#(y,v) -> eq#(s(x),s(y)) -> eq#(x,y)
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