Input TRS: 1: RAo(R()) -> R() 2: RAn(R()) -> R() 3: WAo(W()) -> W() 4: WAn(W()) -> W() 5: Rw() ->= RIn(Rw()) 6: Ww() ->= WIn(Ww()) 7: top(ok(system(r,W(),RIo(x),Ww(),p))) ->= top(check(system(RAo(r),W(),x,Ww(),p))) 8: top(ok(system(r,W(),RIn(x),Ww(),p))) ->= top(check(system(RAn(r),W(),x,Ww(),p))) 9: top(ok(system(R(),W(),Rw(),WIn(y),p))) ->= top(check(system(R(),WAn(W()),Rw(),y,p))) 10: top(ok(system(R(),W(),Rw(),WIo(y),p))) ->= top(check(system(R(),WAo(W()),Rw(),y,p))) 11: top(ok(system(r,W(),RIo(x),y,PR()))) ->= top(check(system(RAo(r),W(),x,y,PW()))) 12: top(ok(system(r,W(),RIn(x),y,PR()))) ->= top(check(system(RAn(r),W(),x,y,PW()))) 13: top(ok(system(R(),W(),x,WIo(y),PW()))) ->= top(check(system(R(),WAo(W()),x,y,PR()))) 14: top(ok(system(R(),W(),x,WIn(y),PW()))) ->= top(check(system(R(),WAn(W()),x,y,PR()))) 15: check(RIo(x)) ->= ok(RIo(x)) 16: check(RAo(x)) ->= RAo(check(x)) 17: check(RAn(x)) ->= RAn(check(x)) 18: check(WAo(x)) ->= WAo(check(x)) 19: check(WAn(x)) ->= WAn(check(x)) 20: check(RIo(x)) ->= RIo(check(x)) 21: check(RIn(x)) ->= RIn(check(x)) 22: check(WIo(x)) ->= WIo(check(x)) 23: check(WIn(x)) ->= WIn(check(x)) 24: check(system(v1,v2,v3,v4,v5)) ->= system(check(v1),v2,v3,v4,v5) 25: check(system(v1,v2,v3,v4,v5)) ->= system(v1,check(v2),v3,v4,v5) 26: check(system(v1,v2,v3,v4,v5)) ->= system(v1,v2,check(v3),v4,v5) 27: check(system(v1,v2,v3,v4,v5)) ->= system(v1,v2,v3,check(v4),v5) 28: check(system(v1,v2,v3,v4,v5)) ->= system(v1,v2,v3,v4,check(v5)) 29: RAo(ok(x)) ->= ok(RAo(x)) 30: RAn(ok(x)) ->= ok(RAn(x)) 31: WAo(ok(x)) ->= ok(WAo(x)) 32: WAn(ok(x)) ->= ok(WAn(x)) 33: RIo(ok(x)) ->= ok(RIo(x)) 34: RIn(ok(x)) ->= ok(RIn(x)) 35: WIo(ok(x)) ->= ok(WIo(x)) 36: WIn(ok(x)) ->= ok(WIn(x)) 37: system(ok(v1),v2,v3,v4,v5) ->= ok(system(v1,v2,v3,v4,v5)) 38: system(v1,ok(v2),v3,v4,v5) ->= ok(system(v1,v2,v3,v4,v5)) 39: system(v1,v2,ok(v3),v4,v5) ->= ok(system(v1,v2,v3,v4,v5)) 40: system(v1,v2,v3,ok(v4),v5) ->= ok(system(v1,v2,v3,v4,v5)) 41: system(v1,v2,v3,v4,ok(v5)) ->= ok(system(v1,v2,v3,v4,v5)) Number of strict rules: 4 Direct Order(PosReal,>,Poly) ... removes: 1 3 10 7 11 13 RAo(x1) weight: (/ 1 16) + x1 RIo(x1) weight: (/ 3 32) + x1 W() weight: (/ 1 16) WIn(x1) weight: x1 top(x1) weight: 2 * x1 PR() weight: (/ 1 16) WAo(x1) weight: (/ 1 16) + 2 * x1 system(x1,x2,x3,x4,x5) weight: (/ 591953 16) + x5 + x4 + x3 + x2 + x1 Ww() weight: 0 WIo(x1) weight: (/ 5 32) + x1 check(x1) weight: x1 ok(x1) weight: x1 Rw() weight: (/ 1 16) R() weight: (/ 1 16) WAn(x1) weight: x1 RIn(x1) weight: x1 PW() weight: (/ 1 16) RAn(x1) weight: x1 Number of strict rules: 2 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #top(ok(system(R(),W(),Rw(),WIn(y),p))) ->? #top(check(system(R(),WAn(W()),Rw(),y,p))) #2: #top(ok(system(R(),W(),Rw(),WIn(y),p))) ->? #check(system(R(),WAn(W()),Rw(),y,p)) #3: #top(ok(system(R(),W(),Rw(),WIn(y),p))) ->? #WAn(W()) #4: #check(system(v1,v2,v3,v4,v5)) ->? #check(v1) #5: #check(WIn(x)) ->? #check(x) #6: #top(ok(system(r,W(),RIn(x),y,PR()))) ->? #top(check(system(RAn(r),W(),x,y,PW()))) #7: #top(ok(system(r,W(),RIn(x),y,PR()))) ->? #check(system(RAn(r),W(),x,y,PW())) #8: #top(ok(system(r,W(),RIn(x),y,PR()))) ->? #RAn(r) #9: #top(ok(system(R(),W(),x,WIn(y),PW()))) ->? #top(check(system(R(),WAn(W()),x,y,PR()))) #10: #top(ok(system(R(),W(),x,WIn(y),PW()))) ->? #check(system(R(),WAn(W()),x,y,PR())) #11: #top(ok(system(R(),W(),x,WIn(y),PW()))) ->? #WAn(W()) #12: #RAn(ok(x)) ->? #RAn(x) #13: #check(system(v1,v2,v3,v4,v5)) ->? #check(v2) #14: #check(RIo(x)) ->? #check(x) #15: #check(system(v1,v2,v3,v4,v5)) ->? #check(v5) #16: #check(WIo(x)) ->? #check(x) #17: #check(system(v1,v2,v3,v4,v5)) ->? #check(v4) #18: #check(RAn(x)) ->? #RAn(check(x)) #19: #check(RAn(x)) ->? #check(x) #20: #check(WAn(x)) ->? #WAn(check(x)) #21: #check(WAn(x)) ->? #check(x) #22: #WAn(ok(x)) ->? #WAn(x) #23: #check(system(v1,v2,v3,v4,v5)) ->? #check(v3) #24: #check(RIn(x)) ->? #check(x) #25: #check(RAo(x)) ->? #check(x) #26: #top(ok(system(r,W(),RIn(x),Ww(),p))) ->? #top(check(system(RAn(r),W(),x,Ww(),p))) #27: #top(ok(system(r,W(),RIn(x),Ww(),p))) ->? #check(system(RAn(r),W(),x,Ww(),p)) #28: #top(ok(system(r,W(),RIn(x),Ww(),p))) ->? #RAn(r) #29: #check(WAo(x)) ->? #check(x) Number of SCCs: 4, DPs: 19, edges: 187 SCC { #22 } Removing DPs: Order(PosReal,>,Sum)... succeeded. RAo(x1) weight: (/ 1 4) + x1 RIo(x1) weight: (/ 1 4) + x1 W() weight: 0 #RAn(x1) weight: 0 WIn(x1) weight: x1 top(x1) weight: 0 PR() weight: 0 #check(x1) weight: 0 #top(x1) weight: 0 WAo(x1) weight: (/ 1 4) + x1 system(x1,x2,x3,x4,x5) weight: (/ 1 4) + x1 + x2 + x3 + x4 + x5 #WAn(x1) weight: x1 Ww() weight: 0 WIo(x1) weight: (/ 1 4) + x1 check(x1) weight: (/ 1 4) + x1 ok(x1) weight: (/ 1 4) + x1 Rw() weight: 0 R() weight: 0 WAn(x1) weight: (/ 1 4) + x1 RIn(x1) weight: x1 PW() weight: 0 RAn(x1) weight: (/ 1 4) + x1 Removed DPs: #22 Number of SCCs: 3, DPs: 18, edges: 186 SCC { #12 } Removing DPs: Order(PosReal,>,Sum)... succeeded. RAo(x1) weight: (/ 1 4) + x1 RIo(x1) weight: (/ 1 4) + x1 W() weight: 0 #RAn(x1) weight: x1 WIn(x1) weight: x1 top(x1) weight: 0 PR() weight: 0 #check(x1) weight: 0 #top(x1) weight: 0 WAo(x1) weight: (/ 1 4) + x1 system(x1,x2,x3,x4,x5) weight: (/ 1 4) + x1 + x2 + x3 + x4 + x5 #WAn(x1) weight: 0 Ww() weight: 0 WIo(x1) weight: (/ 1 4) + x1 check(x1) weight: (/ 1 4) + x1 ok(x1) weight: (/ 1 4) + x1 Rw() weight: 0 R() weight: 0 WAn(x1) weight: (/ 1 4) + x1 RIn(x1) weight: x1 PW() weight: 0 RAn(x1) weight: (/ 1 4) + x1 Removed DPs: #12 Number of SCCs: 2, DPs: 17, edges: 185 SCC { #1 #6 #9 #26 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed. Removing edges: failed. Finding a loop... failed. MAYBE