19.61/15.86 MAYBE 19.61/15.87 Input TRS: 19.61/15.87 AC symbols: virg * 19.61/15.87 1: substt(ef(x),y) -> ef(substt(x,y)) 19.61/15.87 2: substf(Pe(x),y) -> Pe(substt(x,y)) 19.61/15.87 3: substf(neg(f),s) -> neg(substf(f,s)) 19.61/15.87 4: substf(and(f,g),s) -> and(substf(f,s),substf(g,s)) 19.61/15.87 5: substf(or(f,g),s) -> or(substf(f,s),substf(g,s)) 19.61/15.87 6: substf(imp(f,g),s) -> imp(substf(f,s),substf(g,s)) 19.61/15.87 7: substf(forall(f),s) -> forall(substf(f,.(1(),ron(s,shift())))) 19.61/15.87 8: substf(exists(f),s) -> exists(substf(f,.(1(),ron(s,shift())))) 19.61/15.87 9: substt(x,id()) -> x 19.61/15.87 10: substf(f,id()) -> f 19.61/15.87 11: substt(substt(x,s),t) -> substt(x,ron(s,t)) 19.61/15.87 12: substf(substf(f,s),t) -> substf(f,ron(s,t)) 19.61/15.87 13: substt(1(),.(x,s)) -> x 19.61/15.87 14: ron(id(),s) -> s 19.61/15.87 15: ron(shift(),.(x,s)) -> s 19.61/15.87 16: ron(ron(s,t),u) -> ron(s,ron(t,u)) 19.61/15.87 17: ron(.(x,s),t) -> .(substt(x,t),ron(s,t)) 19.61/15.87 18: ron(s,id()) -> s 19.61/15.87 19: .(1(),shift()) -> id() 19.61/15.87 20: .(substt(1(),s),ron(shift(),s)) -> s 19.61/15.87 21: virg(emptyfset(),a) -> a 19.61/15.87 22: virg(a,a) -> a 19.61/15.87 23: *(emptysset(),a) -> a 19.61/15.87 24: *(a,a) -> a 19.61/15.87 25: neg(neg(f)) -> f 19.61/15.87 26: and(f,f) -> f 19.61/15.87 27: or(f,f) -> f 19.61/15.87 28: imp(f,g) -> or(neg(f),g) 19.61/15.87 29: exists(f) -> neg(forall(neg(f))) 19.61/15.87 30: sequent(virg(convf(neg(f)),a),b) -> sequent(a,virg(convf(f),b)) 19.61/15.87 31: sequent(convf(neg(f)),b) -> sequent(emptyfset(),virg(convf(f),b)) 19.61/15.87 32: sequent(a,virg(convf(neg(f)),b)) -> sequent(virg(convf(f),a),b) 19.61/15.87 33: sequent(a,convf(neg(f))) -> sequent(virg(convf(f),a),emptyfset()) 19.61/15.87 34: sequent(virg(convf(and(f,g)),a),b) -> sequent(virg(convf(g),virg(convf(f),a)),b) 19.61/15.87 35: sequent(convf(and(f,g)),b) -> sequent(virg(convf(f),convf(g)),b) 19.61/15.87 36: sequent(a,virg(convf(or(f,g)),b)) -> sequent(a,virg(virg(convf(f),convf(g)),b)) 19.61/15.87 37: sequent(a,convf(or(f,g))) -> sequent(a,virg(convf(f),convf(g))) 19.61/15.87 38: convs(sequent(a,virg(convf(and(f,g)),b))) -> *(convs(sequent(a,virg(convf(f),b))),convs(sequent(a,virg(convf(g),b)))) 19.61/15.87 39: convs(sequent(a,convf(and(f,g)))) -> *(convs(sequent(a,convf(f))),convs(sequent(a,convf(g)))) 19.61/15.87 40: convs(sequent(virg(convf(or(f,g)),a),b)) -> *(convs(sequent(virg(convf(f),a),b)),convs(sequent(virg(convf(g),a),b))) 19.61/15.87 41: convs(sequent(convf(or(f,g)),b)) -> *(convs(sequent(convf(f),b)),convs(sequent(convf(g),b))) 19.61/15.87 42: convs(sequent(virg(convf(f),a),virg(convf(f),b))) -> emptysset() 19.61/15.87 43: convs(sequent(virg(convf(f),a),convf(f))) -> emptysset() 19.61/15.87 44: convs(sequent(convf(f),virg(convf(f),b))) -> emptysset() 19.61/15.87 45: convs(sequent(convf(f),convf(f))) -> emptysset() 19.61/15.87 46: *(convs(sequent(virg(f,a),virg(g,b))),convs(sequent(a,b))) -> convs(sequent(a,b)) 19.61/15.87 47: *(convs(sequent(virg(f,a),b)),convs(sequent(a,b))) -> convs(sequent(a,b)) 19.61/15.87 48: *(convs(sequent(a,virg(f,b))),convs(sequent(a,b))) -> convs(sequent(a,b)) 19.61/15.87 49: *(convs(sequent(virg(f,a),b)),convs(sequent(a,emptyfset()))) -> convs(sequent(a,emptyfset())) 19.61/15.87 50: *(convs(sequent(emptyfset(),b)),convs(sequent(a,virg(f,b)))) -> convs(sequent(emptyfset(),b)) 19.61/15.87 51: *(convs(sequent(emptyfset(),b)),convs(sequent(a,b))) -> convs(sequent(emptyfset(),b)) 19.61/15.87 52: *(convs(sequent(a,emptyfset())),convs(sequent(a,b))) -> convs(sequent(a,emptyfset())) 19.61/15.87 53: *(convs(sequent(emptyfset(),emptyfset())),convs(sequent(a,b))) -> convs(sequent(emptyfset(),emptyfset())) 19.61/15.87 Number of strict rules: 53 19.61/15.87 Direct POLO(bPol) ... failed. 19.61/15.87 Uncurrying ... failed. 19.61/15.87 Dependency Pairs: 19.61/15.87 #1: #substf(Pe(x),y) -> #substt(x,y) 19.61/15.87 #2: #exists(f) -> #neg(forall(neg(f))) 19.61/15.87 #3: #exists(f) -> #neg(f) 19.61/15.87 #4: #sequent(convf(and(f,g)),b) -> #sequent(virg(convf(f),convf(g)),b) 19.61/15.87 #5: #sequent(convf(and(f,g)),b) -> #virg(convf(f),convf(g)) 19.61/15.87 #6: #convs(sequent(convf(or(f,g)),b)) -> #*(convs(sequent(convf(f),b)),convs(sequent(convf(g),b))) 19.61/15.87 #7: #convs(sequent(convf(or(f,g)),b)) -> #convs(sequent(convf(f),b)) 19.61/15.87 #8: #convs(sequent(convf(or(f,g)),b)) -> #sequent(convf(f),b) 19.61/15.87 #9: #convs(sequent(convf(or(f,g)),b)) -> #convs(sequent(convf(g),b)) 19.61/15.87 #10: #convs(sequent(convf(or(f,g)),b)) -> #sequent(convf(g),b) 19.61/15.87 #11: #sequent(a,convf(or(f,g))) -> #sequent(a,virg(convf(f),convf(g))) 19.61/15.87 #12: #sequent(a,convf(or(f,g))) -> #virg(convf(f),convf(g)) 19.61/15.87 #13: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #*(convs(sequent(a,virg(convf(f),b))),convs(sequent(a,virg(convf(g),b)))) 19.61/15.87 #14: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #convs(sequent(a,virg(convf(f),b))) 19.61/15.87 #15: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #sequent(a,virg(convf(f),b)) 19.61/15.87 #16: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #virg(convf(f),b) 19.61/15.87 #17: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #convs(sequent(a,virg(convf(g),b))) 19.61/15.87 #18: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #sequent(a,virg(convf(g),b)) 19.61/15.87 #19: #convs(sequent(a,virg(convf(and(f,g)),b))) -> #virg(convf(g),b) 19.61/15.87 #20: #substf(imp(f,g),s) -> #imp(substf(f,s),substf(g,s)) 19.61/15.87 #21: #substf(imp(f,g),s) -> #substf(f,s) 19.61/15.87 #22: #substf(imp(f,g),s) -> #substf(g,s) 19.61/15.87 #23: #*(x,*(y,z)) ->= #*(*(x,y),z) 19.61/15.87 #24: #*(x,*(y,z)) ->= #*(x,y) 19.61/15.87 #25: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #*(convs(sequent(virg(convf(f),a),b)),convs(sequent(virg(convf(g),a),b))) 19.61/15.87 #26: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #convs(sequent(virg(convf(f),a),b)) 19.61/15.87 #27: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #sequent(virg(convf(f),a),b) 19.61/15.87 #28: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #virg(convf(f),a) 19.61/15.87 #29: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #convs(sequent(virg(convf(g),a),b)) 19.61/15.87 #30: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #sequent(virg(convf(g),a),b) 19.61/15.87 #31: #convs(sequent(virg(convf(or(f,g)),a),b)) -> #virg(convf(g),a) 19.61/15.87 #32: #substt(substt(x,s),t) -> #substt(x,ron(s,t)) 19.61/15.87 #33: #substt(substt(x,s),t) -> #ron(s,t) 19.61/15.87 #34: #substf(substf(f,s),t) -> #substf(f,ron(s,t)) 19.61/15.87 #35: #substf(substf(f,s),t) -> #ron(s,t) 19.61/15.87 #36: #sequent(convf(neg(f)),b) -> #sequent(emptyfset(),virg(convf(f),b)) 19.61/15.87 #37: #sequent(convf(neg(f)),b) -> #virg(convf(f),b) 19.61/15.87 #38: #sequent(virg(convf(neg(f)),a),b) -> #sequent(a,virg(convf(f),b)) 19.61/15.87 #39: #sequent(virg(convf(neg(f)),a),b) -> #virg(convf(f),b) 19.61/15.87 #40: #substf(forall(f),s) -> #substf(f,.(1(),ron(s,shift()))) 19.61/15.87 #41: #substf(forall(f),s) -> #.(1(),ron(s,shift())) 19.61/15.87 #42: #substf(forall(f),s) -> #ron(s,shift()) 19.61/15.87 #43: #convs(sequent(a,convf(and(f,g)))) -> #*(convs(sequent(a,convf(f))),convs(sequent(a,convf(g)))) 19.61/15.87 #44: #convs(sequent(a,convf(and(f,g)))) -> #convs(sequent(a,convf(f))) 19.61/15.87 #45: #convs(sequent(a,convf(and(f,g)))) -> #sequent(a,convf(f)) 19.61/15.87 #46: #convs(sequent(a,convf(and(f,g)))) -> #convs(sequent(a,convf(g))) 19.61/15.87 #47: #convs(sequent(a,convf(and(f,g)))) -> #sequent(a,convf(g)) 19.61/15.87 #48: #sequent(a,convf(neg(f))) -> #sequent(virg(convf(f),a),emptyfset()) 19.61/15.87 #49: #sequent(a,convf(neg(f))) -> #virg(convf(f),a) 19.61/15.87 #50: #substf(or(f,g),s) -> #or(substf(f,s),substf(g,s)) 19.61/15.87 #51: #substf(or(f,g),s) -> #substf(f,s) 19.61/15.87 #52: #substf(or(f,g),s) -> #substf(g,s) 19.61/15.87 #53: #imp(f,g) -> #or(neg(f),g) 19.61/15.87 #54: #imp(f,g) -> #neg(f) 19.61/15.87 #55: #sequent(virg(convf(and(f,g)),a),b) -> #sequent(virg(convf(g),virg(convf(f),a)),b) 19.61/15.87 #56: #sequent(virg(convf(and(f,g)),a),b) -> #virg(convf(g),virg(convf(f),a)) 19.61/15.87 #57: #sequent(virg(convf(and(f,g)),a),b) -> #virg(convf(f),a) 19.61/15.87 #58: #ron(.(x,s),t) -> #.(substt(x,t),ron(s,t)) 19.61/15.87 #59: #ron(.(x,s),t) -> #substt(x,t) 19.61/15.87 #60: #ron(.(x,s),t) -> #ron(s,t) 19.61/15.87 #61: #sequent(a,virg(convf(neg(f)),b)) -> #sequent(virg(convf(f),a),b) 19.61/15.87 #62: #sequent(a,virg(convf(neg(f)),b)) -> #virg(convf(f),a) 19.61/15.87 #63: #sequent(a,virg(convf(or(f,g)),b)) -> #sequent(a,virg(virg(convf(f),convf(g)),b)) 19.61/15.87 #64: #sequent(a,virg(convf(or(f,g)),b)) -> #virg(virg(convf(f),convf(g)),b) 19.61/15.87 #65: #sequent(a,virg(convf(or(f,g)),b)) -> #virg(convf(f),convf(g)) 19.61/15.87 #66: #ron(ron(s,t),u) -> #ron(s,ron(t,u)) 19.61/15.87 #67: #ron(ron(s,t),u) -> #ron(t,u) 19.61/15.87 #68: #substf(neg(f),s) -> #neg(substf(f,s)) 19.61/15.87 #69: #substf(neg(f),s) -> #substf(f,s) 19.61/15.87 #70: #substt(ef(x),y) -> #substt(x,y) 19.61/15.87 #71: #virg(x,virg(y,z)) ->= #virg(virg(x,y),z) 19.61/15.87 #72: #virg(x,virg(y,z)) ->= #virg(x,y) 19.61/15.87 #73: #substf(exists(f),s) -> #exists(substf(f,.(1(),ron(s,shift())))) 19.61/15.87 #74: #substf(exists(f),s) -> #substf(f,.(1(),ron(s,shift()))) 19.61/15.87 #75: #substf(exists(f),s) -> #.(1(),ron(s,shift())) 19.61/15.87 #76: #substf(exists(f),s) -> #ron(s,shift()) 19.61/15.87 #77: #substf(and(f,g),s) -> #and(substf(f,s),substf(g,s)) 19.61/15.87 #78: #substf(and(f,g),s) -> #substf(f,s) 19.61/15.87 #79: #substf(and(f,g),s) -> #substf(g,s) 19.61/15.87 Number of SCCs: 6, DPs: 37 19.61/15.87 SCC { #71 #72 } 19.61/15.87 only weak rules. 19.61/15.87 Number of SCCs: 5, DPs: 35 19.61/15.87 SCC { #23 #24 } 19.61/15.87 only weak rules. 19.61/15.87 Number of SCCs: 4, DPs: 33 19.61/15.87 SCC { #32 #33 #59 #60 #66 #67 #70 } 19.61/15.87 POLO(Sum)... succeeded. 19.61/15.87 #sequent w: 0 19.61/15.87 1 w: 1 19.61/15.87 ron w: x1 + x2 + 1 19.61/15.87 convs w: 0 19.61/15.87 #. w: 0 19.61/15.87 emptyfset w: 0 19.61/15.87 #exists w: 0 19.61/15.87 and w: 0 19.61/15.87 #ron w: x1 19.61/15.87 convf w: 0 19.61/15.87 #substf w: 0 19.61/15.87 #virg w: 0 19.61/15.87 #* w: 0 19.61/15.87 Pe w: 0 19.61/15.87 #substt w: x1 19.61/15.87 substf w: 0 19.61/15.87 forall w: 0 19.61/15.87 virg w: 0 19.61/15.87 #imp w: 0 19.61/15.87 or w: 0 19.61/15.87 neg w: 0 19.61/15.87 . w: x1 + x2 + 1 19.61/15.87 ef w: x1 + 1 19.61/15.87 #convs w: 0 19.61/15.87 emptysset w: 0 19.61/15.87 id w: 4 19.61/15.87 #or w: 0 19.61/15.87 #neg w: 0 19.61/15.87 substt w: x1 + x2 + 1 19.61/15.87 imp w: 0 19.61/15.87 sequent w: 0 19.61/15.87 #and w: 0 19.61/15.87 * w: 0 19.61/15.87 shift w: 1 19.61/15.87 exists w: 0 19.61/15.87 USABLE RULES: { } 19.61/15.87 Removed DPs: #32 #33 #59 #60 #66 #67 #70 19.61/15.87 Number of SCCs: 3, DPs: 26 19.61/15.87 SCC { #21 #22 #34 #40 #51 #52 #69 #74 #78 #79 } 19.61/15.87 POLO(Sum)... succeeded. 19.61/15.87 #sequent w: 0 19.61/15.87 1 w: 1 19.61/15.87 ron w: x1 + x2 + 1 19.61/15.87 convs w: 0 19.61/15.87 #. w: 0 19.61/15.87 emptyfset w: 0 19.61/15.87 #exists w: 0 19.61/15.87 and w: x1 + x2 + 1 19.61/15.87 #ron w: 0 19.61/15.87 convf w: 0 19.61/15.87 #substf w: x1 + x2 19.61/15.87 #virg w: 0 19.61/15.87 #* w: 0 19.61/15.87 Pe w: 0 19.61/15.87 #substt w: 0 19.61/15.87 substf w: x1 + x2 + 2 19.61/15.87 forall w: x1 + 4 19.61/15.87 virg w: 0 19.61/15.87 #imp w: 0 19.61/15.87 or w: x1 + x2 + 1 19.61/15.87 neg w: x1 + 1 19.61/15.87 . w: x2 + 1 19.61/15.87 ef w: x1 + 1 19.61/15.87 #convs w: 0 19.61/15.87 emptysset w: 0 19.61/15.87 id w: 2 19.61/15.87 #or w: 0 19.61/15.87 #neg w: 0 19.61/15.87 substt w: 1 19.61/15.87 imp w: x1 + x2 + 1 19.61/15.87 sequent w: 0 19.61/15.87 #and w: 0 19.61/15.87 * w: 0 19.61/15.87 shift w: 1 19.61/15.87 exists w: x1 + 4 19.61/15.87 USABLE RULES: { 14..20 } 19.61/15.87 Removed DPs: #21 #22 #34 #40 #51 #52 #69 #74 #78 #79 19.61/15.87 Number of SCCs: 2, DPs: 16 19.61/15.87 SCC { #4 #11 #36 #38 #48 #55 #61 #63 } 19.61/15.87 POLO(Sum)... succeeded. 19.61/15.87 #sequent w: x1 + x2 19.61/15.87 1 w: 1 19.61/15.87 ron w: x1 + x2 + 1 19.61/15.87 convs w: 0 19.61/15.87 #. w: 0 19.61/15.87 emptyfset w: 1 19.61/15.87 #exists w: 0 19.61/15.87 and w: x1 + x2 + 2 19.61/15.87 #ron w: 0 19.61/15.87 convf w: x1 + 1 19.61/15.87 #substf w: x2 19.61/15.87 #virg w: 0 19.61/15.87 #* w: 0 19.61/15.87 Pe w: 0 19.61/15.87 #substt w: 0 19.61/15.87 substf w: 2 19.61/15.87 forall w: 4 19.61/15.87 virg w: x1 + x2 19.61/15.87 #imp w: 0 19.61/15.87 or w: x1 + x2 + 2 19.61/15.87 neg w: x1 + 2 19.61/15.87 . w: x2 + 1 19.61/15.87 ef w: x1 + 1 19.61/15.87 #convs w: 0 19.61/15.87 emptysset w: 0 19.61/15.87 id w: 2 19.61/15.87 #or w: 0 19.61/15.87 #neg w: 0 19.61/15.87 substt w: 1 19.61/15.87 imp w: 1 19.61/15.87 sequent w: 0 19.61/15.87 #and w: 0 19.61/15.87 * w: 0 19.61/15.87 shift w: 1 19.61/15.87 exists w: 4 19.61/15.87 USABLE RULES: { 14..22 54 } 19.61/15.87 Removed DPs: #4 #11 #36 #38 #48 #55 #61 #63 19.61/15.87 Number of SCCs: 1, DPs: 8 19.61/15.87 SCC { #7 #9 #14 #17 #26 #29 #44 #46 } 19.61/15.87 POLO(Sum)... succeeded. 19.61/15.87 #sequent w: x1 + x2 19.61/15.87 1 w: 1 19.61/15.87 ron w: x1 + x2 + 1 19.61/15.87 convs w: 0 19.61/15.87 #. w: 0 19.61/15.87 emptyfset w: 1 19.61/15.87 #exists w: 0 19.61/15.87 and w: x1 + x2 + 1 19.61/15.87 #ron w: 0 19.61/15.87 convf w: x1 + 1 19.61/15.87 #substf w: x2 19.61/15.87 #virg w: 0 19.61/15.87 #* w: 0 19.61/15.87 Pe w: 0 19.61/15.87 #substt w: 0 19.61/15.87 substf w: 2 19.61/15.87 forall w: 4 19.61/15.87 virg w: x1 + x2 19.61/15.87 #imp w: 0 19.61/15.87 or w: x1 + x2 + 1 19.61/15.87 neg w: x1 + 1 19.61/15.87 . w: x2 + 1 19.61/15.87 ef w: x1 + 1 19.61/15.87 #convs w: x1 19.61/15.87 emptysset w: 0 19.61/15.87 id w: 2 19.61/15.87 #or w: 0 19.61/15.87 #neg w: 0 19.61/15.87 substt w: 1 19.61/15.87 imp w: 1 19.61/15.87 sequent w: x1 + x2 19.61/15.87 #and w: 0 19.61/15.87 * w: 0 19.61/15.87 shift w: 1 19.61/15.87 exists w: 4 19.61/15.87 USABLE RULES: { 14..22 30..37 54 } 19.61/15.87 Removed DPs: #7 #9 #14 #17 #26 #29 #44 #46 19.61/15.87 Number of SCCs: 0, DPs: 0 19.61/15.87 Next Dependency Pairs: 19.61/15.87 #80: #*(*(convs(sequent(virg(f,a),virg(g,b))),convs(sequent(a,b))),_1) -> #*(convs(sequent(a,b)),_1) 19.61/15.87 #81: #*(*(convs(sequent(virg(f,a),b)),convs(sequent(a,b))),_1) -> #*(convs(sequent(a,b)),_1) 19.61/15.87 #82: #*(*(convs(sequent(emptyfset(),emptyfset())),convs(sequent(a,b))),_1) -> #*(convs(sequent(emptyfset(),emptyfset())),_1) 19.61/15.87 #83: #*(*(convs(sequent(a,virg(f,b))),convs(sequent(a,b))),_1) -> #*(convs(sequent(a,b)),_1) 19.61/15.87 #84: #*(x,*(y,z)) ->= #*(*(x,y),z) 19.61/15.87 #85: #*(x,*(y,z)) ->= #*(x,y) 19.61/15.87 #86: #*(*(convs(sequent(emptyfset(),b)),convs(sequent(a,b))),_1) -> #*(convs(sequent(emptyfset(),b)),_1) 19.61/15.87 #87: #*(*(a,a),_1) -> #*(a,_1) 19.61/15.87 #88: #*(*(emptysset(),a),_1) -> #*(a,_1) 19.61/15.87 #89: #*(*(convs(sequent(a,emptyfset())),convs(sequent(a,b))),_1) -> #*(convs(sequent(a,emptyfset())),_1) 19.61/15.87 #90: #*(*(convs(sequent(virg(f,a),b)),convs(sequent(a,emptyfset()))),_1) -> #*(convs(sequent(a,emptyfset())),_1) 19.61/15.87 #91: #virg(virg(a,a),_1) -> #virg(a,_1) 19.61/15.87 #92: #virg(virg(emptyfset(),a),_1) -> #virg(a,_1) 19.61/15.87 #93: #virg(x,virg(y,z)) ->= #virg(virg(x,y),z) 19.61/15.87 #94: #virg(x,virg(y,z)) ->= #virg(x,y) 19.61/15.87 #95: #*(*(convs(sequent(emptyfset(),b)),convs(sequent(a,virg(f,b)))),_1) -> #*(convs(sequent(emptyfset(),b)),_1) 19.61/15.87 Number of SCCs: 2, DPs: 16 19.61/15.87 SCC { #91..94 } 19.61/15.87 POLO(Sum)... succeeded. 19.61/15.87 #sequent w: x1 + x2 19.61/15.87 1 w: 1 19.61/15.87 ron w: x1 + x2 + 1 19.61/15.87 convs w: 0 19.61/15.87 #. w: 0 19.61/15.87 emptyfset w: 1 19.61/15.87 #exists w: 0 19.61/15.87 and w: x1 + x2 + 2 19.61/15.87 #ron w: 0 19.61/15.87 convf w: x1 + 1 19.61/15.87 #substf w: x2 19.61/15.87 #virg w: x1 + x2 19.61/15.87 #* w: 0 19.61/15.87 Pe w: 0 19.61/15.87 #substt w: 0 19.61/15.87 substf w: 2 19.61/15.87 forall w: 4 19.61/15.87 virg w: x1 + x2 + 1 19.61/15.87 #imp w: 0 19.61/15.87 or w: x1 + x2 + 2 19.61/15.87 neg w: x1 + 2 19.61/15.87 . w: x2 + 1 19.61/15.87 ef w: x1 + 1 19.61/15.87 #convs w: x1 19.61/15.87 emptysset w: 0 19.61/15.87 id w: 2 19.61/15.87 #or w: 0 19.61/15.87 #neg w: 0 19.61/15.87 substt w: 1 19.61/15.87 imp w: 1 19.61/15.87 sequent w: x1 + x2 19.61/15.87 #and w: 0 19.61/15.87 * w: 0 19.61/15.87 shift w: 1 19.61/15.87 exists w: 4 19.61/15.87 USABLE RULES: { 14..22 30..37 54 } 19.61/15.87 Removed DPs: #91 #92 #94 19.61/15.87 Number of SCCs: 2, DPs: 13 19.61/15.87 SCC { #93 } 19.61/15.87 only weak rules. 19.61/15.87 Number of SCCs: 1, DPs: 12 19.61/15.87 SCC { #80..90 #95 } 19.61/15.87 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 19.61/15.87 Finding a loop... failed. 19.61/15.87 EOF